Category:Abstract Algebra

A

• [+] Algebraic Geometry‎ (2 C, 4 P)
• [+] Algebraic Number Theory‎ (2 C, 11 P)
• [+] Algebras‎ (1 C, 12 P)

B

• [×] Boolean Rings‎ (7 P)

C

• [+] Commutative Algebra‎ (1 C, 30 P)
• [×] Constant Operation‎ (3 P)

E

• [×] Entropic Structures‎ (2 P)
• [×] External Direct Product‎ (13 P)

F

• [+] Field Theory‎ (12 C, 43 P)

G

• [+] Galois Theory‎ (1 C, 5 P)
• [+] Group Theory‎ (22 C, 92 P)

H

• [+] Homomorphisms‎ (10 C, 25 P)

I

• [+] Integral Domains‎ (4 C, 57 P)
• [×] Internal Direct Products‎ (2 P)
• [×] Invariant Theory‎ (1 P)
• [+] Inverse Completions‎ (1 C, 18 P)

K

• [×] Kummer Theory‎ (empty)

L

• [×] Left and Right Operations‎ (16 P)
• [×] Linear Transformations‎ (29 P)

M

• [×] Magmas‎ (3 P)
• [×] Max and Min Operations‎ (19 P)
• [+] Module Theory‎ (6 C, 22 P)

M cont.

• [×] Modulo Arithmetic‎ (66 P)
• [+] Monoids‎ (1 C, 44 P)

N

• [×] Naturally Ordered Semigroup‎ (37 P)
• [+] Numbers‎ (9 C, 9 P)

P

• [×] Peano's Axioms‎ (7 P)

R

• [×] Representation Theory‎ (10 P)
• [+] Ring Theory‎ (22 C, 54 P)

S

• [+] Semigroups‎ (5 C, 68 P)
• [×] Sequences‎ (15 P)
• [×] Subset Products‎ (26 P)

T

• [×] Tensor Theory‎ (empty)

A

• Associative and Anticommutative
• Associative Idempotent Anticommutative
• Associativity and Commutativity Properties
• Associativity on Four Elements
• Associativity on Indexing Set

C

• Cancellable in Subset
• Count of Binary Operations on a Set
• Count of Binary Operations with Fixed Identity
• Count of Binary Operations with Identity
• Count of Binary Operations Without Identity
• Count of Commutative Binary Operations on a Set
• Count of Commutative Binary Operations with Fixed Identity
• Count of Commutative Binary Operations with Identity

D

• Diagonal Relation is Universally Compatible

E

• Equality of Algebraic Structures
• External Direct Product Distributivity
• External Direct Product Projection and Canonical Injection
• External Direct Product Projection and Canonical Injection/General Result

F

• Frobenius's Theorem
• Frobenius's Theorem/Lemma 1
• Frobenius's Theorem/Lemma 2

G

• General Associativity Theorem
• General Associativity Theorem/Alternative Formulation
• General Associativity Theorem/Formal Statement
• General Commutativity Theorem
• General Distributivity Theorem
• General Operation from a Binary Operation

I

• Identities all Self-Inverse
• Identities are Idempotent
• Identity is Unique
• Identity of Power Set with Intersection
• Identity of Power Set with Union
• Identity Only Idempotent Cancellable Element
• Induced Structure Associative
• Induced Structure Commutative
• Induced Structure Distributive

I cont.

• Induced Structure Identity
• Induced Structure Inverse
• Inverses Not Always Unique for Non-Associative Operation

L

• Left and Right Identity the Same
• Left and Right Zero the Same

M

• Mappings to Algebraic Structure form Similar Algebraic Structure
• Mappings to R-Algebraic Structure form Similar R-Algebraic Structure
• More than One Left Identity then No Right Identity
• More than One Right Zero then No Left Zero

R

• Restriction of Operation Associativity
• Restriction of Operation Commutativity
• Restriction of Operation Distributivity

T

• Trichotomy Law

U

• Upper Semilattice on Classical Set is Semilattice

Z

• Zero Element is Unique
• Zero of Power Set with Intersection
• Zero of Power Set with Union