Category:Definitions/Abstract Algebra
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This category contains definitions related to Abstract Algebra.
Related results can be found in Category: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 92 subcategories, out of 92 total.
A
- Definitions/Additive Groups (2 P)
- Definitions/Associativity (2 P)
B
C
- Definitions/Cancellability (19 P)
- Definitions/Cayley Tables (4 P)
D
- Definitions/Discriminants (2 P)
E
- Definitions/Epimorphisms (9 P)
F
G
- Definitions/Galois Theory (13 P)
H
I
- Definitions/Idempotence (13 P)
- Definitions/Invariant Theory (2 P)
K
- Definitions/Kronecker Delta (4 P)
- Definitions/Kummer Theory (1 P)
L
- Definitions/Left Operation (1 P)
- Definitions/Lie Theory (1 P)
M
- Definitions/Magmas of Sets (1 P)
- Definitions/Max Operation (3 P)
- Definitions/Min Operation (2 P)
- Definitions/Monoid Rings (4 P)
N
O
- Definitions/One (6 P)
P
- Definitions/Parenthesization (2 P)
- Definitions/Peano's Axioms (8 P)
- Definitions/Products (16 P)
Q
R
- Definitions/Restrictions (22 P)
- Definitions/Right Operation (1 P)
S
- Definitions/Semirings (2 P)
- Definitions/Square Mapping (4 P)
T
U
- Definitions/Unity (5 P)
V
W
Z
- Definitions/Zero (11 P)
- Definitions/Zero Elements (3 P)
Pages in category "Definitions/Abstract Algebra"
The following 196 pages are in this category, out of 196 total.
A
- Definition:Absorb
- Definition:Absorbing Element
- Definition:Absorption Law
- Definition:Abstract Algebra
- Definition:Additive Function (Conventional)
- Definition:Additive Group
- Definition:Additive Inverse
- Definition:Additive Notation
- Definition:Algebra (Abstract Algebra)
- Definition:Algebra Loop
- Definition:Algebraic Structure
- Definition:Algebraic Substructure
- Definition:Algebraic System
- Definition:Algebraic Topology
- Definition:Alternative Operation
- Definition:Antiassociative Operation
- Definition:Antiassociative Structure
- Definition:Anticommutative
- Definition:Antihomomorphism
- Definition:Archimedean Property
- Definition:Archimedean Property/Norm
- Definition:Archimedean Property/Ordering
- Definition:Associative Algebraic Structure
- Definition:Associative Operation
- Definition:Associative Word on Set
- Definition:Automorphism (Abstract Algebra)
C
- Definition:Cancellable
- Definition:Cancellable Element
- Definition:Cancellable Operation
- Definition:Cayley Table
- Definition:Closed Algebraic Structure
- Definition:Commutative
- Definition:Commutative Algebra (Mathematical Branch)
- Definition:Commutator
- Definition:Composite Defined by Permutation
- Definition:Congruence Relation
- Definition:Constant Operation
- Definition:Coprime
- Definition:Cross Cancellation Property
- Definition:Cross-Relation
- Definition:Cross-Relation on Natural Numbers
D
E
- Definition:Empty Sum
- Definition:Endomorphism
- Definition:Endomorphism Ring of Abelian Group
- Definition:Entropic
- Definition:Entropic Operation
- Definition:Epimorphism (Abstract Algebra)
- Definition:Extension of Operation
- Definition:External Direct Product
- Definition:External Direct Product/General Definition
- Definition:External Direct Product/Structures with Two Operations
F
G
H
I
- Definition:Idempotence
- Definition:Idempotent Algebraic Structure
- Definition:Idempotent Element
- Definition:Idempotent Operation
- Definition:Identity (Abstract Algebra)
- Definition:Induced Operation
- Definition:Induced Structure
- Definition:Infinite Order
- Definition:Infinite Order (Structure)
- Definition:Infinite Structure
- Definition:Internal Direct Product
- Definition:Invariant Theory
- Definition:Inverse (Abstract Algebra)
- Definition:Inverse Completion
- Definition:Inverse of Subset
- Definition:Invertible Element
- Definition:Invertible Operation
- Definition:Involution
- Definition:Isomorphism (Abstract Algebra)
K
L
M
N
O
- Definition:Operation Induced by Direct Product/General Definition
- Definition:Operation Induced by Injection
- Definition:Operation Induced by Permutation
- Definition:Operation Induced by Restriction
- Definition:Operation Induced on Power Set
- Definition:Operation Induced on Quotient Set
- Definition:Order of Structure
- Definition:Order of Structure/Finite Structure
- Definition:Order of Structure/Infinite Structure
- Definition:Ordered Ring Automorphism
- Definition:Ordered Ring Monomorphism
- Definition:Ordered Structure
- Definition:Ordered Tuple on Set
P
- Definition:Pairwise Coprime
- Definition:Parenthesization
- Definition:Permutable Elements
- Definition:Permutation Theory
- Definition:Pointwise Operation
- Definition:Polynomial Evaluation Homomorphism
- Definition:Polynomial Evaluation Homomorphism/Multiple Indeterminates
- Definition:Polynomial Evaluation Homomorphism/Single Indeterminate
- Definition:Polynomial Theory
- Definition:Positive Definite
- Definition:Power of Element
- Definition:Power-Associative Operation
- Definition:Product (Abstract Algebra)
- Definition:Product Inverse Operation
- Definition:Product Notation (Algebra)
- Definition:Properties of Algebraic Structures of One Operation
- Definition:Properties of Algebraic Structures of Two Operations
R
S
- Definition:Self-Distributive Operation
- Definition:Self-Inverse Element
- Definition:Sequence
- Definition:Sequence with Finite Support
- Definition:Series
- Definition:Series/General
- Definition:Series/General/Sequence of Partial Products
- Definition:Set of Literals
- Definition:Set of Words
- Definition:Setwise Addition
- Definition:Square
- Definition:Square/Mapping
- Definition:Strictly Negative
- Definition:Strictly Positive
- Definition:Structure Induced by Permutation
- Definition:Subadditive Function (Conventional)
- Definition:Subband
- Definition:Subset Product
- Definition:Subset Product with Singleton
- Definition:Subset Product/Singleton
- Definition:Summation
- Definition:Support of Element of Direct Product
- Definition:Support of Mapping to Algebraic Structure
- Definition:Support of Sequence in Algebraic Structure
- Definition:Symmetric Element