Category:Definitions/Ring Theory
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This category contains definitions related to Ring Theory.
Related results can be found in Category:Ring Theory.
Ring Theory is a branch of abstract algebra which studies rings and other related algebraic structures.
Subcategories
This category has the following 32 subcategories, out of 32 total.
A
- Definitions/Associates (9 P)
B
- Definitions/Boolean Rings (2 P)
- Definitions/Bézout Domains (3 P)
C
- Definitions/Centralizers (9 P)
D
E
F
G
- Definitions/Graded Rings (3 P)
I
- Definitions/Ideals of Rings (2 P)
L
N
- Definitions/Noetherian Rings (5 P)
- Definitions/Normed Rings (2 P)
O
P
R
- Definitions/Ring Extensions (3 P)
- Definitions/Ring Homomorphisms (24 P)
- Definitions/Rings of Mappings (10 P)
- Definitions/Rings of Sequences (12 P)
S
- Definitions/Subtraction (29 P)
T
U
- Definitions/Units of Rings (4 P)
Pages in category "Definitions/Ring Theory"
The following 191 pages are in this category, out of 191 total.
A
- Definition:Addition/Ring
- Definition:Additive Function on UFD
- Definition:Additive Group of Field
- Definition:Additive Group of Ring
- Definition:Additive Identity
- Definition:Additive Inverse in Field
- Definition:Additive Inverse in Ring
- Definition:Additive Inverse/Ring
- Definition:Additive Semiring
- Definition:Additive Subgroup
- Definition:Algebraic Element of Ring Extension
- Definition:Annihilator of Ring
- Definition:Artinian Ring
- Definition:Ascending Chain Condition on Ideals
- Definition:Ascending Chain Condition/Ideals
- Definition:Associate
- Definition:Atom (Ring Theory)
C
- Definition:Cancellable Semiring
- Definition:Category of Rings
- Definition:Category of Rings with Unity
- Definition:Center (Abstract Algebra)
- Definition:Center (Abstract Algebra)/Ring
- Definition:Center of Ring
- Definition:Centralizer
- Definition:Characteristic of Ring
- Definition:Common Divisor
- Definition:Commutative Algebra (Mathematical Branch)
- Definition:Commutative and Unitary Ring
- Definition:Commutative Division Ring
- Definition:Commutative Ring
- Definition:Commutative Ring with Unity
- Definition:Commutative Semiring
- Definition:Commutator/Ring
- Definition:Completely Additive Function
- Definition:Cyclotomic Ring
D
G
- Definition:Gaussian Domain
- Definition:Generated Subring
- Definition:Generator of Division Subring
- Definition:Generator of Ideal of Ring
- Definition:Generator of Ring
- Definition:Generator of Subring
- Definition:Gradation Compatible with Ring Structure
- Definition:Graded Ring
- Definition:Group of Units
- Definition:Group of Units of Ring
- Definition:Group of Units/Ring
- Definition:Group Ring
H
I
- Definition:Ideal of Ring
- Definition:Ideal Theory
- Definition:Idempotent Ring
- Definition:Integral Multiple of Ring Element
- Definition:Integral Multiple/Rings and Fields
- Definition:Internal Direct Product of Rings
- Definition:Internal Direct Sum of Rings
- Definition:Internal Direct Sum of Rings/Direct Summand
- Definition:Irreducible Element of Ring
M
N
- Definition:Negative of Element
- Definition:Nilpotent Ring Element
- Definition:Nilradical of Ring
- Definition:Nilradical of Ring/Definition 1
- Definition:Nilradical of Ring/Definition 2
- Definition:Noetherian Ring
- Definition:Non-Commutative Ring
- Definition:Non-Null Ring
- Definition:Non-Trivial Ring
- Definition:Non-Zero-Divisor
- Definition:Nontrivial Ring
- Definition:Nonzero Ring Element
- Definition:Norm on Ring
- Definition:Norm/Ring
- Definition:Norm/Ring/Multiplicative
- Definition:Norm/Ring/Submultiplicative
- Definition:Normed Ring
- Definition:Null Ring
P
- Definition:Polynomial Equation
- Definition:Polynomial Function
- Definition:Polynomial Function/General Definition
- Definition:Polynomial over Ring as Function on Free Monoid on Set
- Definition:Polynomial Ring over Sequences
- Definition:Positive Characteristic
- Definition:Positive Definite (Ring)
- Definition:Positivity Property
- Definition:Power of Element/Ring
- Definition:Power of Ring Element
- Definition:Primal
- Definition:Prime Element of Ring
- Definition:Product (Abstract Algebra)/Ring
- Definition:Product Inverse
- Definition:Proper Divisor
- Definition:Proper Element of Ring
- Definition:Proper Subring
- Definition:Proper Zero Divisor
R
- Definition:Reduced Ring
- Definition:Regular Element of Ring
- Definition:Rig
- Definition:Right Zero Divisor
- Definition:Ring (Abstract Algebra)
- Definition:Ring (Abstract Algebra)/Addition
- Definition:Ring (Abstract Algebra)/Also known as
- Definition:Ring (Abstract Algebra)/Binding Priority
- Definition:Ring (Abstract Algebra)/Product
- Definition:Ring (Abstract Algebra)/Ring Less Zero
- Definition:Ring Addition
- Definition:Ring Direct Product
- Definition:Ring Direct Product/Finite Case
- Definition:Ring Extension
- Definition:Ring Homomorphism
- Definition:Ring Less Zero
- Definition:Ring Negative
- Definition:Ring of Idempotents
- Definition:Ring of Integers
- Definition:Ring of Mappings
- Definition:Ring of Quaternions
- Definition:Ring of Sequences
- Definition:Ring of Square Matrices
- Definition:Ring Product
- Definition:Ring Product Inverse
- Definition:Ring Subtraction
- Definition:Ring Theory
- Definition:Ring with Unity
- Definition:Ring Zero
- Definition:Ringoid (Abstract Algebra)
- Definition:Rng
- Definition:Root of Mapping
- Definition:Root of Polynomial
S
- Definition:Schreier Domain
- Definition:Semihereditary Ring
- Definition:Semiring (Abstract Algebra)
- Definition:Skew Field
- Definition:Spectrum of Ring
- Definition:Subdomain
- Definition:Subfield
- Definition:Submultiplicative Function on Ring
- Definition:Submultiplicative Norm on Ring
- Definition:Subring
- Definition:Subsemiring
- Definition:Subtraction
- Definition:Subtraction/Field
- Definition:Subtraction/Ring
- Definition:Sum of Ideals of Ring
T
- Definition:Topological Division Ring
- Definition:Topological Ring
- Definition:Transcendental
- Definition:Transcendental (Abstract Algebra)
- Definition:Transcendental (Abstract Algebra)/Ring
- Definition:Transcendental over Integral Domain
- Definition:Trivial Annihilator
- Definition:Trivial Gradation
- Definition:Trivial Ring
- Definition:Two Ring