Category:Abstract Algebra

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This category contains results about Abstract Algebra.
Definitions specific to this category can be found in Definitions/Abstract Algebra.

Abstract algebra is a branch of mathematics which studies algebraic structures and algebraic systems.

It can be roughly described as the study of sets equipped with operations.

Subcategories

This category has the following 113 subcategories, out of 113 total.

A

Absorption Laws‎ (12 P)
Additive Functions‎ (4 C, 7 P)
Additive Groups‎ (empty)
Additive Inverses‎ (empty)
Algebra Loops‎ (2 C, 4 P)
Algebraic Closure‎ (4 C, 29 P)
Algebraic Geometry‎ (9 C, 20 P)
Algebraic Number Theory‎ (4 C, 16 P)
Algebraic Structures‎ (16 C, 2 P)
Algebraic Topology‎ (3 C, 10 P)
Algebras‎ (5 C, 23 P)
Antiassociative Structures‎ (3 P)
Anticommutativity‎ (1 C, 5 P)
Antihomomorphisms‎ (empty)
Associativity‎ (7 C, 22 P)
Automorphism Groups‎ (1 C, 8 P)

B

Boolean Algebras‎ (2 C, 25 P)

C

Cancellability‎ (7 C, 33 P)
Category Theory‎ (19 C, 65 P)
Cayley Tables‎ (2 C, 8 P)
Centers (Abstract Algebra)‎ (1 C)
Closed Algebraic Structures‎ (1 C, 9 P)
Commutative Algebra‎ (16 C, 50 P)
Commutative Semigroups‎ (3 C, 7 P)
Commutativity‎ (13 C, 50 P)
Compatible Relations‎ (7 C, 34 P)
Constant Operation‎ (6 P)
Coprimality‎ (1 C)
Count of Binary Operations on Set‎ (1 C, 2 P)
Count of Binary Operations with Fixed Identity‎ (2 P)
Count of Binary Operations with Identity‎ (1 C, 2 P)
Count of Binary Operations with Zero‎ (2 P)
Count of Binary Operations Without Identity‎ (2 P)
Count of Commutative Binary Operations on Set‎ (1 C, 2 P)
Count of Commutative Binary Operations with Fixed Identity‎ (2 P)
Count of Commutative Binary Operations with Identity‎ (2 P)

D

Differential Algebra‎ (empty)
Direct Products‎ (9 C, 9 P)
Direct Sums‎ (1 P)
Discriminants‎ (empty)
Distributive Operations‎ (5 C, 19 P)
Divisibility‎ (5 C, 10 P)
Divisors‎ (23 C, 69 P)

E

Entropic Operations‎ (2 C, 1 P)
Entropic Structures‎ (2 C, 12 P)
Equality‎ (6 C, 16 P)
Examples of Abstract Algebra‎ (1 P)
Examples of Isomorphisms‎ (2 C, 5 P)
Examples of Words‎ (3 P)
External Direct Products‎ (6 C, 23 P)

F

Field Theory‎ (40 C, 61 P)
Formal Laurent Series‎ (empty)
Frobenius's Theorem‎ (6 P)

G

Galois Theory‎ (1 C, 9 P)
General Distributivity Theorem‎ (6 P)
Group Rings‎ (1 P)
Group Theory‎ (101 C, 98 P)

H

Homological Algebra‎ (3 C, 19 P)
Homomorphisms‎ (11 C, 33 P)
Huntington Algebras‎ (empty)

I

Idempotence‎ (6 C, 25 P)
Identity Elements‎ (7 C, 38 P)
Index Laws‎ (39 P)
Integral Domains‎ (18 C, 54 P)
Internal Direct Products‎ (1 C, 7 P)
Invariant Theory‎ (empty)
Inverse Completions‎ (3 C, 22 P)
Inverse Elements‎ (11 C, 35 P)
Inverse of Product‎ (1 C, 7 P)
Isomorphisms‎ (23 C, 38 P)

K

Kummer Theory‎ (empty)

L

Lattice Theory‎ (15 C, 31 P)
Left Operation‎ (1 C, 19 P)
Linear Transformations‎ (16 C, 77 P)

M

Magmas of Sets‎ (5 P)
Max and Min Operations‎ (2 C, 4 P)
Module Theory‎ (34 C, 64 P)
Modulo Arithmetic‎ (28 C, 72 P)
Monoid Rings‎ (empty)

N

Nilpotence‎ (1 P)
Numbers‎ (32 C, 24 P)

O

Operations‎ (1 C, 2 P)
Operations Induced by Permutations‎ (7 P)
Ordered Structures‎ (8 C, 4 P)

P

Parenthesization‎ (6 P)
Peano's Axioms‎ (12 P)
Pointwise Operations‎ (6 C, 26 P)
Polynomial Theory‎ (37 C, 116 P)
Powers (Abstract Algebra)‎ (1 C, 20 P)
Product Inverse Operation‎ (11 P)
Products‎ (3 C, 16 P)

R

Regular Representations‎ (1 C, 23 P)
Representation Theorems‎ (3 C, 3 P)
Representation Theory‎ (11 P)
Restrictions‎ (3 C, 39 P)
Right Operation‎ (1 C, 20 P)
Ring Theory‎ (57 C, 91 P)
Roots of Unity‎ (1 C, 11 P)

S

Self-Distributive Operations‎ (3 C, 10 P)
Self-Inverse Elements‎ (3 P)
Semidirect Products‎ (4 P)
Sequences‎ (34 C, 36 P)
Square Mapping‎ (empty)
Subset Products‎ (9 C, 36 P)
Summations‎ (14 C, 91 P)

T

Tensor Theory‎ (1 C)
Transplants‎ (1 C, 7 P)
Trichotomy Law‎ (1 C, 4 P)

U

Unity‎ (empty)

V

Vector Algebra‎ (20 C, 29 P)

W

Words (Abstract Algebra)‎ (1 P)

Z

Zero‎ (1 C, 6 P)
Zero Elements‎ (10 P)

Pages in category "Abstract Algebra"

The following 31 pages are in this category, out of 31 total.

A

C

E

F

G

I

K

L

Left Cancellable Element is Left Cancellable in Subset

M

P

Q

Quotient Theorem

R

T

Trichotomy Law

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