Pages that link to "Definition:Closure (Abstract Algebra)/Algebraic Structure"
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The following pages link to Definition:Closure (Abstract Algebra)/Algebraic Structure:
Displayed 22 items.
- User:Jshflynn/Definition:Linguistic structure (← links)
- User:Jshflynn/Kleene Star is Linguistic Structure (← links)
- User:Jshflynn/P-star is Commutative Monoid under Union (← links)
- User:Jshflynn/Hungerford Algebra (← links)
- User:Ascii/Definitions (← links)
- User:Ascii/Definitions (by Meaning) (← links)
- User:Ascii/Definitions (by Meaning 1-200) (← links)
- User:Ascii/Definitions (by Meaning 1-300) (← links)
- User:Ascii/Definitions (by Meaning 1-400) (← links)
- User:Ascii/Definitions (by Meaning 1-500) (← links)
- User:Ascii/Definitions (by Meaning 1-600) (← links)
- User:Ascii/Definitions (by Meaning 1-700) (← links)
- User:Ascii/Definitions (by Meaning 1-800) (← links)
- Help:Redirects (← links)
- Category:Algebraic Closure (transclusion) (← links)
- Category:Closed Algebraic Structures (transclusion) (← links)
- Category:Definitions/Algebraic Closure (transclusion) (← links)
- Definition:Closure (Abstract Algebra) (transclusion) (← links)
- Definition:Closed Algebraic Structure (redirect page) (← links)
- One-Step Subgroup Test (← links)
- Two-Step Subgroup Test (← links)
- Intersection of Subsemigroups (← links)
- Cancellable Elements of Semigroup form Subsemigroup (← links)
- Subgroup of Cyclic Group is Cyclic (← links)
- Equivalence of Axiom Schemata for Groups (← links)
- Group has Latin Square Property (← links)
- Restriction of Associative Operation is Associative (← links)
- Idempotent Magma Element forms Singleton Submagma (← links)
- Magma Subset Product with Self (← links)
- Test for Submonoid (← links)
- Equivalence of Definitions of Self-Inverse (← links)
- Invertible Elements of Monoid form Subgroup of Cancellable Elements (← links)
- Trivial Relation is Universally Congruent (← links)
- External Direct Product Closure (← links)
- Morphism Property Preserves Closure (← links)
- Restriction of Homomorphism to Image is Epimorphism (← links)
- Epimorphism Preserves Semigroups (← links)
- Monomorphism Image is Isomorphic to Domain (← links)
- Set of Homomorphisms to Abelian Group is Subgroup of All Mappings (← links)
- Embedding Theorem (← links)
- Subset Product defining Inverse Completion of Commutative Semigroup is Commutative Semigroup (← links)
- Inverse Completion of Commutative Semigroup is Abelian Group (← links)
- Identity is only Idempotent Element in Group (← links)
- Power Structure of Group is Semigroup (← links)
- Group Homomorphism of Product with Inverse (← links)
- Opposite Group is Group (← links)
- Group Example: x inv c y (← links)
- Symmetric Difference on Power Set forms Abelian Group (← links)
- Identity of Subgroup (← links)
- Union of Subgroups (← links)
- Ring Less Zero is Semigroup for Product iff No Proper Zero Divisors (← links)
- Subring Test (← links)
- Ideal of Unit is Whole Ring (← links)
- Test for Ideal (← links)
- Epimorphism Preserves Rings (← links)
- Finite Integral Domain is Galois Field (← links)
- Conjugate of Subgroup is Subgroup (← links)
- Intersection with Normal Subgroup is Normal (← links)
- Coset Product is Well-Defined (← links)
- Ring Homomorphism Preserves Subrings (← links)
- Symmetric Difference with Intersection forms Ring (← links)
- Existence of Field of Quotients (← links)
- External Direct Product of Groups is Group (← links)
- Integer Multiplication is Closed (← links)
- Modulo Addition is Closed (← links)
- Modulo Multiplication is Closed (← links)
- Cancellable Finite Semigroup is Group (← links)
- Finite Subgroup Test (← links)
- Set of Words Generates Group (← links)
- Internal Direct Product Theorem (← links)
- Direct Product of Central Subgroup with Inverse Isomorphism is Central Subgroup (← links)
- Group/Examples/x+y over 1+xy (← links)
- Group/Examples/Self-Inverse and Cancellable Elements (← links)
- Non-Zero Real Numbers under Multiplication form Abelian Group (← links)
- Integers Modulo m under Addition form Cyclic Group (← links)
- Reduced Residue System under Multiplication forms Abelian Group (← links)
- Quotient of Transformation Group acts Effectively (← links)
- Second Sylow Theorem (← links)
- Finite Submodule of Function Space (← links)
- Matrix Space Semigroup under Hadamard Product (← links)
- General Linear Group is Group (← links)
- Field of Characteristic Zero has Unique Prime Subfield (← links)
- Polynomials Closed under Addition (← links)
- Complex Addition is Closed (← links)
- Complex Multiplication is Closed (← links)
- Homotopy Group is Group (← links)
- Dicyclic Group is Non-Abelian Group (← links)
- Inverse Completion Less Zero of Integral Domain is Closed (← links)
- Real Addition is Closed (← links)
- Real Multiplication is Closed (← links)
- Properties of Hadamard Product (← links)
- Set System Closed under Intersection is Commutative Semigroup (← links)
- Set System Closed under Union is Commutative Semigroup (← links)
- Set System Closed under Symmetric Difference is Abelian Group (← links)
- Equivalence of Definitions of Algebra of Sets (← links)
- Sigma-Algebra is Delta-Algebra (← links)
- Associativity on Four Elements (← links)
- Product of Commuting Elements with Inverses (← links)
- Pointwise Addition on Continuous Real Functions forms Group (← links)
- Symmetry Group of Equilateral Triangle is Group (← links)
- Quotient Group is Group (← links)
- Subtraction on Numbers is Anticommutative (← links)
- Subset Product Action is Group Action (← links)
- Set of All Relations is a Monoid (← links)
- Integer Multiples Closed under Addition (← links)
- Integer Multiples Closed under Multiplication (← links)
- Non-Zero Integers Closed under Multiplication (← links)
- Left and Right Operation are Closed for All Subsets (← links)
- Two-Step Subgroup Test using Subset Product (← links)
- Symmetric Group is Group (← links)
- Quaternion Addition forms Abelian Group (← links)
- Sum of All Ring Products is Closed under Addition (← links)
- Properties of Integers (← links)
- Integer Addition is Closed (← links)
- Properties of Natural Numbers (← links)
- Properties of Rational Numbers (← links)
- Properties of Real Numbers (← links)
- Properties of Complex Numbers (← links)
- Rational Addition is Closed (← links)
- Rational Multiplication is Closed (← links)
- Free Commutative Monoid is Commutative Monoid (← links)
- Natural Number Addition is Closed (← links)
- Integer Subtraction is Closed (← links)
- Rational Subtraction is Closed (← links)
- Real Subtraction is Closed (← links)
- Complex Subtraction is Closed (← links)
- Strictly Positive Real Numbers are Closed under Division (← links)
- Quadratic Integers over 2 form Subdomain of Reals (← links)
- Integers form Ordered Integral Domain (← links)
- Real Numbers of Type Rational a plus b root 2 form Field (← links)
- Valuation Ring is Local (← links)
- Discrete Topology is Topology (← links)
- Continuous Functions on Compact Space form Banach Space (← links)
- One-Step Vector Subspace Test (← links)
- Real Numbers under Addition Modulo 1 form Group (← links)
- Galois Group is Group (← links)
- Kernel is Trivial iff Monomorphism/Group (← links)
- Equivalence of Definitions of Integral Domain (← links)
- Power Set is Closed under Set Difference (← links)
- Center of Group is Subgroup (← links)
- Quotient Theorem for Group Homomorphisms (← links)
- Subgroup of Solvable Group is Solvable (← links)
- Min Operation on Toset forms Semigroup (← links)
- Set of Linear Subspaces is Closed under Intersection (← links)
- Linear Subspaces Closed under Setwise Addition (← links)
- Non-Zero Natural Numbers under Multiplication form Commutative Semigroup (← links)
- Isomorphism Preserves Semigroups (← links)
- Product is Left Identity Therefore Left Cancellable (← links)
- Product is Right Identity Therefore Right Cancellable (← links)
- Integer Multiples Greater than Positive Integer Closed under Addition (← links)
- Integer Multiples Greater than Positive Integer Closed under Multiplication (← links)
- Non-Zero Rational Numbers Closed under Multiplication (← links)
- Non-Zero Real Numbers Closed under Multiplication (← links)
- Non-Zero Complex Numbers are Closed under Multiplication (← links)
- Non-Zero Modulo Numbers Closed under Multiplication then Modulo is Prime (← links)
- Magma is Submagma of Itself (← links)
- Empty Set is Submagma of Magma (← links)
- Max Operation on Toset forms Semigroup (← links)
- Automorphism Group is Subgroup of Symmetric Group (← links)
- Null Space Closed under Vector Addition (← links)
- Dynkin System with Generator Closed under Intersection is Sigma-Algebra (← links)
- Coset Product is Well-Defined/Proof 1 (← links)
- Power Function on Complex Numbers is Epimorphism (← links)
- External Direct Product of Groups is Group/Finite Product (← links)
- Structure Induced by Group Operation is Group (← links)
- Construction of Inverse Completion/Quotient Structure is Commutative Semigroup (← links)
- Construction of Inverse Completion/Image of Quotient Mapping is Subsemigroup (← links)
- Trivial Ring is Commutative Ring (← links)
- Quotient Ring is Ring (← links)
- Non-Trivial Commutative Division Ring is Field (← links)
- Finite Integral Domain is Galois Field/Proof 2 (← links)
- Field of Characteristic Zero has Unique Prime Subfield/Proof 2 (← links)
- Subgroup of Cyclic Group is Cyclic/Proof 1 (← links)
- Center of Group is Subgroup/Proof 1 (← links)
- Sigma-Algebra is Monotone Class (← links)
- Modulo Addition is Closed/Integers (← links)
- Modulo Addition is Closed/Real Numbers (← links)
- Ring Homomorphism Preserves Subrings/Proof 2 (← links)
- Ring Homomorphism Preserves Subrings/Proof 3 (← links)
- Uniqueness of Product Measures (← links)
- Group Induces B-Algebra (← links)
- B-Algebra Induces Group (← links)
- Subset Product of Subgroups/Sufficient Condition/Proof 1 (← links)
- Subset Product of Subgroups/Sufficient Condition (← links)
- Natural Number Multiplication is Closed (← links)
- Symmetric Difference with Intersection forms Ring/Proof 2 (← links)
- Group is Normal in Itself (← links)
- Monoid Category is Category (← links)
- Ordinal Exponentiation is Closed (← links)
- Closure for Finite Collection of Relations and Operations (← links)
- Isomorphism Preserves Semigroups/Proof 1 (← links)
- Symmetric Group is Group/Proof 1 (← links)
- Set of Words Generates Group/Corollary (← links)
- Non-Zero Complex Numbers are Closed under Multiplication/Proof 1 (← links)
- Non-Zero Complex Numbers are Closed under Multiplication/Proof 2 (← links)
- Complex Multiplication is Closed/Proof 1 (← links)
- Complex Multiplication is Closed/Proof 2 (← links)
- Inclusion Mapping on Subgroup is Homomorphism (← links)
- Multiindices under Addition form Commutative Monoid (← links)
- Ring of Idempotents is Idempotent Ring (← links)
- Field is Integral Domain/Proof 1 (← links)
- External Direct Product Closure/General Result (← links)
- Union of Relations Compatible with Operation is Compatible (← links)
- Intersection of Relations Compatible with Operation is Compatible (← links)
- Inverse of Relation Compatible with Operation is Compatible (← links)
- Power Set with Union and Intersection forms Boolean Algebra (← links)
- Duality Principle (Boolean Algebras) (← links)
- Power Structure of Group is Semigroup/Proof 1 (← links)
- Square of Number Always Exists (← links)
- Trivial Gradation is Gradation (← links)
- Ring of Polynomial Forms is Commutative Ring with Unity (← links)
- Quadratic Integers over 2 form Subdomain of Reals/Proof 1 (← links)
- Product of Commuting Idempotent Elements is Idempotent (← links)
- Set of all Self-Maps under Composition forms Semigroup (← links)
- Polynomials Closed under Addition/Polynomials over Integral Domain/Proof 1 (← links)
- Polynomials Closed under Addition/Polynomials over Integral Domain (← links)
- Polynomials Closed under Addition/Polynomials over Ring (← links)
- Polynomials Closed under Addition/Polynomials over Integral Domain/Proof 2 (← links)
- Ring of Polynomial Functions is Commutative Ring with Unity (← links)
- Equivalence of Definitions of Boolean Algebra (← links)
- Delta-Algebra is Sigma-Algebra (← links)
- Equivalence of Axiom Schemata for Groups/Warning (← links)
- Reduced Residue System under Multiplication forms Abelian Group/Proof 2 (← links)
- Element Commutes with Square in Semigroup (← links)
- Rational Multiplication is Closed/Proof 1 (← links)
- Rational Multiplication is Closed/Proof 2 (← links)
- Semigroup is Group Iff Latin Square Property Holds (← links)
- Rational Numbers with Denominators Coprime to Prime under Addition form Group (← links)
- Ring of Integers Modulo m is Ring (← links)
- Integers under Multiplication do not form Group (← links)
- Integers under Multiplication form Semigroup (← links)
- Set of Rational Numbers whose Numerator Divisible by p is Closed under Addition (← links)
- Integers under Addition form Abelian Group (← links)
- Set of Rational Numbers whose Numerator Divisible by p is Closed under Multiplication (← links)
- Real Numbers under Addition form Monoid (← links)
- Complex Numbers under Addition form Monoid (← links)
- Rational Numbers under Multiplication form Monoid (← links)
- Real Numbers under Multiplication form Monoid (← links)
- Complex Numbers under Multiplication form Monoid (← links)
- Group has Latin Square Property/Proof 3 (← links)
- Semigroup is Group Iff Latin Square Property Holds/Proof 1 (← links)
- Finite Monoid with Right Cancellable Operation is Group (← links)
- Finite Monoid with Left Cancellable Operation is Group (← links)
- Multiplicative Group of Field is Abelian Group (← links)
- Multiplicative Group of Field is Abelian Group/Proof 1 (← links)
- Affine Group of One Dimension is Group (← links)
- Index in Subgroup (← links)
- Equivalence of Definitions of Ring of Sets (← links)
- Empty Set and Set form Algebra of Sets (← links)
- Equivalence of Definitions of Sigma-Ring (← links)
- Equivalence of Definitions of Sigma-Algebra (← links)
- Rational Division is Closed (← links)
- Complex Addition is Closed/Proof 1 (← links)
- Complex Addition is Closed/Proof 2 (← links)
- Non-Zero Complex Numbers are Closed under Multiplication/Proof 3 (← links)
- Common Ratio in Rational Geometric Sequence is Rational (← links)
- Closure of Pointwise Operation on Algebraic Structure (← links)
- Isomorphism between Roots of Unity under Multiplication and Integers under Modulo Addition (← links)
- Symmetry Group of Square is Group (← links)
- Subset not necessarily Submagma (← links)
- Closed Subsets of Symmetry Group of Square (← links)
- Left Cancellable Elements of Semigroup form Subsemigroup (← links)
- Right Cancellable Elements of Semigroup form Subsemigroup (← links)
- Left Congruence Modulo Subgroup is Equivalence Relation (← links)
- Right Congruence Modulo Subgroup is Equivalence Relation (← links)
- Non-Zero Real Numbers Closed under Multiplication/Proof 1 (← links)
- Non-Zero Real Numbers Closed under Multiplication/Proof 2 (← links)
- Natural Numbers under Multiplication form Semigroup (← links)
- Modulo Multiplication on Reduced Residue System is Closed (← links)
- Reduced Residue System under Multiplication forms Abelian Group/Proof 3 (← links)
- Equivalence of Axiom Schemata for Finite Group (← links)
- Group Generated by Reciprocal of z and 1 minus z (← links)
- Circle Group is Group (← links)
- Circle Group is Group/Proof 3 (← links)
- Non-Zero Real Numbers under Multiplication form Abelian Group/Proof 1 (← links)
- Strictly Positive Real Numbers are Closed under Multiplication (← links)
- Intersection of Submodules is Submodule/General Result (← links)
- Equivalence of Definitions of Generated Submodule over Ring with Unity (← links)
- Subtraction on Numbers is Anticommutative/Integral Domains (← links)
- Natural Number Subtraction is not Closed (← links)
- Subsemigroup/Examples/2x2 Matrices with One Non-Zero Entry (← links)
- Semigroup/Examples/x+y-xy on Integers (← links)
- Subsemigroup/Examples/x+y-xy on Integers (← links)
- Non-Zero Real Numbers under Multiplication form Group (← links)
- Finite Subgroup Test/Proof 1 (← links)
- Finite Subgroup Test/Proof 2 (← links)
- Equivalence of Definitions of Cyclic Group (← links)
- Subgroup/Examples/Natural Numbers in Multiplicative Group of Real Numbers (← links)
- Order of Element in Group equals its Order in Subgroup (← links)
- Subset Product/Examples (← links)
- Group Isomorphism/Examples/Order 2 Matrices with 1 Real Variable (← links)
- Trivial Group is Group (← links)
- Symmetry Group of Line Segment is Group (← links)
- Subgroup Action is Group Action (← links)
- Monoid/Examples/x+y+xy on Reals (← links)
- Group/Examples/x+y+xy over Reals less -1 (← links)
- Group/Examples/Linear Functions (← links)
- Union Operation on Supersets of Subset is Closed (← links)
- Intersection Operation on Supersets of Subset is Closed (← links)
- Subset of Abelian Group Generated by Product of Element with Inverse Element is Subgroup (← links)
- Non-Zero Integers under Multiplication are not Subgroup of Reals (← links)
- Condition for Elements of Group to be in Subgroup (← links)
- Conjugate of Subgroup is Subgroup/Proof 1 (← links)
- Integers under Subtraction do not form Group (← links)
- Group/Examples/x+y+2 over Reals (← links)
- Odd Integers under Multiplication do not form Group (← links)
- Square Matrices with +1 or -1 Determinant under Multiplication forms Group (← links)
- Symmetric Group on 3 Letters/Subgroups/Examples/Non-Subgroup (← links)
- Union of Subgroups/Examples (← links)
- Union of Subgroups/Examples/Subgroups of S3 (← links)
- Master Code forms Vector Space (← links)
- Affine Group of One Dimension is Group/Proof 1 (← links)
- Group of Order 35 is Cyclic Group (← links)
- Group of Order 35 is Cyclic Group/Proof 2 (← links)
- Unity of Subring is not necessarily Unity of Ring (← links)
- Ideal of Ring/Examples/Order 2 Matrices with some Zero Entries (← links)
- Ideal of Ring/Examples/Order 2 Matrices with some Zero Entries/Proof 1 (← links)
- Equivalence of Definitions of Prime Ideal of Commutative and Unitary Ring (← links)
- Ring of Square Matrices over Real Numbers/Examples/2 x 2 (← links)
- Ring of Polynomial Forms over Field is Vector Space/Corollary (← links)
- Simple Algebraic Field Extension consists of Polynomials in Algebraic Number (← links)
- Closure of Hadamard Product (← links)
- Matrix Entrywise Addition over Ring is Closed (← links)
- Non-Zero Complex Numbers under Multiplication form Group (← links)
- Real Numbers under Addition form Group (← links)
- Complex Numbers under Addition form Group (← links)
- Strictly Positive Rational Numbers are Closed under Addition (← links)
- Set of Cuts under Addition forms Abelian Group (← links)
- Set of Cuts forms Ordered Field (← links)
- Imaginary Numbers under Multiplication do not form Group (← links)
- Set of Isometries in Complex Plane under Composition forms Group (← links)
- Set of Affine Mappings on Real Line under Composition forms Group (← links)
- Set of Transpositions is not Subgroup of Symmetric Group (← links)
- Order-Preserving Mapping Not Always Semilattice Homomorphism (← links)
- Join Semilattice Ordered Subset Not Always Subsemilattice (← links)
- Matrix Entrywise Addition over Ring is Closed/Proof 1 (← links)
- Matrix Entrywise Addition over Ring is Closed/Proof 2 (← links)
- Strictly Positive Real Numbers are not Closed under Subtraction (← links)
- Odd Integers under Addition do not form Group (← links)
- Semigroup/Examples/x+y+xy on Positive Integers (← links)
- Inclusion-Exclusion Principle/Examples/3 Events in Event Space (← links)
- Rational Numbers whose Denominators are not Divisible by 4 do not form Ring (← links)
- Order 2 Square Matrices with Zero Diagonals do not form Ring (← links)
- Set of Order m times n Matrices does not form Ring (← links)
- Set of Isometries in Euclidean Space under Composition forms Group (← links)
- Linear Mappings between Vector Spaces form Vector Space (← links)
- Construction of Direct Product of Fields (← links)
- Field has Characteristic of Zero iff exists Monomorphism from Rationals (← links)
- Intersection of Submonoids with Monoid Identity is Submonoid (← links)
- Embedding Theorem/Corollary (← links)
- Left Operation is Closed for All Subsets (← links)
- Right Operation is Closed for All Subsets (← links)
- Integers form Ordered Integral Domain/Proof 1 (← links)
- Preimage of Submodule under Linear Transformation is Submodule (← links)
- Ring of Linear Operators is Ring (← links)
- Group Direct Product/Examples/R-0 x R (← links)
- Subsemigroup of Ordered Semigroup is Ordered (← links)
- Positive Rational Numbers are Closed under Addition (← links)
- Positive Rational Numbers under Addition form Ordered Semigroup (← links)
- Positive Rational Numbers under Addition form Ordered Semigroup/Proof 1 (← links)
- Positive Rational Numbers under Addition form Ordered Semigroup/Proof 2 (← links)
- Positive Rational Numbers under Addition form Commutative Monoid (← links)
- Natural Numbers with Extension fulfil Naturally Ordered Semigroup Axioms 1, 3 and 4/Lemma 1 (← links)
- Closed Algebraic Structure/Examples (← links)
- Closed Algebraic Structure/Examples/2^m 3^n under Multiplication (← links)
- Product Inverse Operation Properties induce Group (← links)
- Product Inverse Operation Properties/Lemma 1 (← links)
- Product Inverse Operation Properties (← links)
- Product Inverse Operation Properties/Lemma 2 (← links)
- Product Inverse Operation Properties/Lemma 3 (← links)
- Product Inverse Operation Properties/Lemma 4 (← links)
- Product Inverse Operation Properties/Lemma 5 (← links)
- Structure Induced by Permutation on Semigroup is not necessarily Semigroup (← links)
- Structure under Right Operation is Semigroup (← links)
- Structure under Left Operation is Semigroup (← links)
- Condition for Group given Semigroup with Idempotent Element (← links)
- Conditions under which Commutative Semigroup is Group (← links)
- Dipper Semigroup is Commutative Semigroup (← links)
- Existence of Subgroup of Dipper Semigroup (← links)
- Group/Examples/ac, ad+b on Positive Reals by Reals (← links)
- Strictly Positive Real Numbers are Closed under Multiplication/Proof 1 (← links)
- Strictly Positive Real Numbers are Closed under Multiplication/Proof 2 (← links)
- Set of Associating Elements forms Subsemigroup of Magma (← links)
- Subset Product/Examples/Congruence Modulo Initial Segment of Natural Numbers (← links)
- Power Structure Operation on Set of Singleton Subsets is Closed (← links)
- Set of Finite Subsets under Induced Operation is Closed (← links)
- Power Structure of Subset is Closed iff Subset is Closed (← links)
- Set of Subsemigroups of Commutative Semigroup form Subsemigroup of Power Structure (← links)
- Equivalence Relation inducing Closed Quotient Set of Magma is Congruence Relation (← links)
- Set of Normal Subgroups of Group is Subsemigroup of Power Set Semigroup (← links)
- Set of Normal Subgroups of Group is Subsemigroup of Power Set under Intersection (← links)
- Condition for Subgroup of Power Set of Group to be Quotient Group (← links)
- Condition for Partition between Invertible and Non-Invertible Elements to induce Congruence Relation on Monoid (← links)
- Condition on Congruence Relations for Cancellable Monoid to be Group (← links)
- Idempotent Semigroup/Examples/Relation induced by Inverse Element/Properties/1 (← links)
- Riesz-Markov-Kakutani Representation Theorem (← links)
- Riesz-Markov-Kakutani Representation Theorem/Lemma 8 (← links)
- Idempotent Semigroup/Examples/Relation induced by Inverse Element/Properties/6 (← links)
- External Direct Product Closure/Sufficient Condition (← links)
- External Direct Product Closure/Necessary Condition (← links)
- Condition for Mapping between Structure and Cartesian Product of Substructures to be Bijection (← links)
- Mapping on Cartesian Product of Substructures is Restriction of Operation (← links)
- Codomain of Internal Direct Isomorphism is Subset Product of Factors (← links)
- Internal Direct Product Theorem/Proof 1 (← links)
- Entropic Structure with Identity is Commutative Monoid (← links)
- Set of Closed Subsets of Power Structure of Entropic Structure is Closed (← links)
- Set of Endomorphisms on Entropic Structure is Closed in Induced Structure on Set of Self-Maps (← links)
- Set of Endomorphisms on Entropic Structure is Closed in Induced Structure on Set of Self-Maps/Converse (← links)
- Condition for Mapping between Structures to be Homomorphism (← links)
- Subgroup of Solvable Group is Solvable/Proof 3 (← links)
- Pointwise Addition on Continuous Real Functions on Closed Unit Interval forms Group (← links)
- Pointwise Addition on Differentiable Real Functions on Closed Unit Interval forms Group (← links)
- Generator of Subsemigroup/Examples/Positive Odd Numbers (← links)
- Subset of Join Semilattice on Total Ordering is Closed (← links)
- Total Semilattice has Unique Total Ordering (← links)
- Natural Numbers under Min Operation forms Total Semilattice (← links)
- Integers Modulo m under Max Operation form Ordered Semigroup (← links)
- Structure Induced by Semigroup Operation is Semigroup (← links)
- Conditions for Ordering in Ordered Group to be Directed (← links)
- Set of Idempotent Elements of Entropic Structure is Closed (← links)
- Union of Sigma-Algebras may not be Sigma-Algebra (← links)
- Event of Stopping Time Equal to Infinity is Measurable in Limit of Filtration/Discrete Time (← links)
- Event of Stopping Time Equal to Infinity is Measurable in Limit of Filtration/Continuous Time (← links)
- Characterization of Stopping Times with respect to Right-Limit Filtration (← links)
- Generated Submodule may not equal Set of Linear Combinations (← links)
- Algebra of Sets is Closed under Intersection (← links)
- Algebra of Sets is Closed under Set Difference (← links)
- Algebra of Sets contains Underlying Set (← links)
- Algebra of Sets is Closed under Intersection/Proof 1 (← links)
- Algebra of Sets is Closed under Intersection/Proof 2 (← links)
- Algebra of Sets contains Underlying Set/Proof 2 (← links)
- Algebra of Sets is Closed under Set Difference/Proof 1 (← links)
- Algebra of Sets is Boolean Algebra (← links)
- Structure Induced by Semilattice Operation is Semilattice (← links)
- Lattice of Continuous Functions is Sublattice of All Real-Valued Functions (← links)
- Lattice of Bounded Continuous Functions is Sublattice of Continuous Real-Valued Functions (← links)
- Gaussian Integers are Closed under Addition (← links)
- Gaussian Integers are Closed under Negation (← links)
- Gaussian Integers are Closed under Subtraction (← links)
- Gaussian Integers are Closed under Multiplication (← links)
- Gaussian Integers are not Closed under Division (← links)
- Kernel of Linear Transformation is Linear Subspace (← links)
- Integers under Subtraction form Magma (← links)
- Natural Numbers under Subtraction do not form Magma (← links)
- Talk:Example:Antiassociative Structure (← links)
- Talk:Finite Integral Domain is Galois Field/Proof 2 (← links)
- Talk:Main Page/Archive 16 (← links)
- User:Jshflynn/P-star is Commutative Monoid under Union (← links)
- User:Jshflynn/P-star is Monoid under Language Product (← links)
- User:Jshflynn/Howson Handbook (← links)
- User:Ybab321/Sandbox/Notes (← links)
- User:Ascii/ProofWiki Sampling Notes for Theorems/Number Theory (← links)
- User:Ascii/Definitions (by Meaning 1-800) (← links)
- User:Caliburn/s/mt/Uniqueness of Product Measures (← links)
- Template:Axiom (← links)
- Template:SemigroupAxiom (← links)
- Template:Algebra-of-sets-axiom (← links)
- Category:Semigroups (← links)
- Category:Definitions/Semigroups (← links)
- Category:Magmas (← links)
- Category:Internal Direct Products (← links)
- Category:Sigma-Algebras (← links)
- Category:Definitions/Sigma-Algebras (← links)
- Category:Boolean Algebras (← links)
- Category:Huntington Algebras (← links)
- Category:Compatible Relations (← links)
- Category:Definitions/Compatible Relations (← links)
- Category:Definitions/Boolean Algebras (← links)
- Category:Examples of Semigroups (← links)
- Category:Rings of Sets (← links)
- Category:Algebras of Sets (← links)
- Category:Sigma-Rings (← links)
- Category:Definitions/Examples of Rings (← links)
- Category:Examples of Rings (← links)
- Category:Definitions/Magmas (← links)
- Category:Lie Algebras (← links)
- Category:Definitions/Sigma-Rings (← links)
- Category:Definitions/Rings of Sets (← links)
- Category:Definitions/Algebras of Sets (← links)
- Category:Examples of Magmas (← links)
- Category:Algebraic Closure (transclusion) (← links)
- Category:Definitions/Examples of Semigroups (← links)
- Category:Definitions/Internal Direct Products (← links)
- Category:Closed Algebraic Structures (transclusion) (← links)
- Category:Sublattices (← links)
- Category:Definitions/Sublattices (← links)
- Category:Total Semilattices (← links)
- Category:Definitions/Algebraic Closure (transclusion) (← links)
- Category:Examples of Sigma-Algebras (← links)
- Category:Axioms/Algebras of Sets (← links)
- Category:Axioms/Ring of Sets Axioms (← links)
- Category:Axioms/Sigma-Ring Axioms (← links)
- Category:Axioms/Sigma-Algebra Axioms (← links)
- Category:Definitions/Subalgebras (← links)
- Category:Subalgebras (← links)
- Category:Definitions/Lie Algebras (← links)
- Axiom:Ring Axioms (← links)
- Axiom:Group Axioms (← links)
- Axiom:Field Axioms (← links)
- Axiom:Abelian Group Axioms (← links)
- Axiom:Group Axioms/Right (← links)
- Axiom:Group Axioms/Left (← links)
- Axiom:Boolean Ring Axioms (← links)
- Axiom:Boolean Algebra/Axioms/Formulation 1 (← links)
- Axiom:Boolean Algebra/Axioms/Formulation 2 (← links)
- Axiom:Monoid Axioms (← links)
- Axiom:Semigroup Axioms (← links)
- Axiom:Ordered Semigroup Axioms (← links)
- Axiom:Ordered Group Axioms (← links)
- Axiom:Real Number/Axioms (← links)
- Axiom:Commutative and Unitary Ring/Axioms (← links)
- Axiom:Additive Semiring Axioms (← links)
- Axiom:Finite Group/Axioms (← links)
- Axiom:Semilattice Axioms (← links)
- Axiom:Product Inverse Operation Axioms (← links)
- Axiom:Bounded Lattice Axioms (← links)
- Axiom:Lattice Axioms (← links)
- Axiom:Sigma-Algebra Axioms (← links)
- Axiom:Algebra of Sets Axioms (← links)
- Definition:Closed Operation (redirect page) (← links)
- Subsemigroup Closure Test (← links)
- Polynomials Closed under Addition (← links)
- Complex Addition is Closed (← links)
- Ring of Sets is Commutative Ring (← links)
- Function of Discrete Random Variable (← links)
- Structure Induced by Ring Operations is Ring (← links)
- Polynomial Ring of Sequences is Ring (← links)
- Field Adjoined Set (← links)
- Brahmagupta-Fibonacci Identity/Extension (← links)
- Join Semilattice is Semilattice (← links)
- Meet Semilattice is Semilattice (← links)
- Power Structure of Magma is Magma (← links)
- Neighborhood Sub-Basis Criterion for Filter Convergence (← links)
- Polynomials Closed under Addition/Polynomial Forms (← links)
- Ring of Polynomial Functions is Commutative Ring with Unity (← links)
- Quotient Structure of Semigroup is Semigroup (← links)
- Quotient Structure is Similar to Structure (← links)
- Natural Numbers Bounded Below under Addition form Commutative Semigroup (← links)
- Closure of Union and Complement imply Closure of Set Difference (← links)
- Complex Addition is Closed/Proof 1 (← links)
- Complex Addition is Closed/Proof 2 (← links)
- Closure of Pointwise Operation on Algebraic Structure (← links)
- Brahmagupta-Fibonacci Identity/General (← links)
- Brahmagupta-Fibonacci Identity/Extension/General (← links)
- Natural Number Subtraction is not Closed (← links)
- Existence of Magma with no Proper Submagma (← links)
- Non-Commutative Ring with Unity and 2 Ideals not necessarily Division Ring (← links)
- Odd Integers do not form Integral Domain (← links)
- Sum of Cuts is Cut (← links)
- Product of Positive Cuts is Positive Cut (← links)
- Product of Cuts is Cut (← links)
- Sum of Rational Cuts is Rational Cut (← links)
- Product of Rational Cuts is Rational Cut (← links)
- Odd Integers under Addition do not form Subgroup of Integers (← links)
- Real Division is not Closed (← links)
- Construction of Direct Product of Fields (← links)
- Operation Induced by Permutation on Magma is Closed (← links)
- Condition for Isomorphism between Structures Induced by Permutations (← links)
- Count of Operations on Finite Set which are Closed on Every Subset (← links)
- Count of Commutative Operations on Finite Set which are Closed on Every Subset (← links)
- Generator of Subsemigroup/Examples/Positive Odd Numbers (← links)
- Intersection of Submagmas is Largest Submagma (← links)
- Structure with Commutative Idempotent Associative Operations satisfying Absorption Laws is Lattice (← links)
- Dipper Operation is Closed on Initial Segment (← links)
- Restriction of Dipper Operation to Non-Zero Initial Segment is Closed (← links)
- Equivalence of Definitions of Join Semilattice (← links)
- User:Abcxyz/Sandbox/Real Numbers/Real Addition is Closed (← links)
- User:Abcxyz/Sandbox/Real Numbers/Real Multiplication is Closed (← links)
- Help:Redirects (← links)
- Definition:Universally Compatible Relation (← links)
- Definition:Universally Congruent (← links)
- Definition:Operation (← links)
- Definition:Clopen Set (← links)
- Definition:Cycle (Graph Theory) (← links)
- Definition:Operation/Binary Operation (← links)
- Definition:Operation/Unary Operation (← links)
- Definition:Binary Operation/Also defined as (← links)
- Definition:Closed under Operation (redirect page) (← links)
- Submodule Test (← links)
- Real Addition is Closed (← links)
- Pointwise Minimum of Stopping Times is Stopping Time (← links)
- Pointwise Infimum of Stopping Times is Stopping Time (← links)
- Pointwise Maximum of Stopping Times is Stopping Time (← links)
- Pointwise Supremum of Stopping Times is Stopping Time (← links)
- Sum of Stopping Times is Stopping Time (← links)
- Stopped Sigma-Algebra is Sigma-Algebra (← links)
- Stopped Sigma-Algebra preserves Inequality between Stopping Times (← links)
- Adapted Stochastic Process at Stopping Time is Measurable with respect to Stopped Sigma-Algebra (← links)
- Least Time at which Discrete-Time Adapted Stochastic Process equals or exceeds Real Number is Stopping Time (← links)
- Stopped Sigma-Algebra of Pointwise Minimum of Stopping Times (← links)
- Definition:Operation/Binary Operation (← links)
- Definition talk:Regular Expression (← links)
- Book:Gaisi Takeuti/Introduction to Axiomatic Set Theory (← links)