Category:Abstract Algebra Definitions

A

• Abelian group
• Absolute value (object)
• Additive function
• Associative

B

• Basis (linear algebra)

C

• C-ring
• Canonical linear map
• Canonical projection of an equivalence relation
• Canonical projection of the equivalence relation
• Cartesian product
• Characteristic of a ring
• Commutative
• Commutator
• Commutator subgroup
• Completely invariant under
• Conjugation
• Coproduct (module)
• Coset
• Cover
• Cu-ring
• Cyclic subgroup

D

• Direct product (module)
• Direct product module
• Direct sum (ring)
• Direct sum module

E

• Equivalence class
• Equivalence classes
• Equivalence relation
• Equivalence relations
• External direct sum module
• External direct sum of modules

F

• Field
• Formal linear combination
• Formal linear combination/Definition
• Free monoid generated by
• Free semigroup generated by
• Free vector space generated by
• Function terminology

G

• Generated subgroup

G cont.

• Generator
• Geometrically independent set
• Group
• Group action
• Group homomorphism
• Group/New page
• Groups

H

• Homomorphism
• Homomorphism (group)
• Homomorphism (module)

I

• Identity map
• Integers
• Integral domain
• Invariant of an equivalence relation
• Invariant under
• Isomorphic (group)
• Isomorphism (group)
• Isomorphism (module)

K

• Kernel
• Klein-4 group

L

• Linear functional
• Linear functionals
• Linear maps

M

• Module
• Module homomorphism
• Module homomorphisms
• Monoid
• Monomial
• Multilinear maps

N

• Normal subgroup

O

• Ordered integral domain
• Ordered pairs
• Orthogonal vectors

P

• Partial order
• Partial ordering
• Partition
• Partition (abstract algebra)
• Passing-to-the-quotient (function)
• Permutation

P cont.

• Permutation of a set
• Permutation on a set
• Polynomial u-ring
• Poset
• Preorder
• Preordering
• Preset

Q

• Q-ring
• Quotient
• Quotient (function)
• Quotient (group)
• Quotient by an equivalence relation
• Quotient group
• Quotient module
• Quotient vector space

R

• R-module
• Ring
• Ring homomorphism
• Ring with identity
• Ring with unity
• Ring/New page
• Rings

S

• Semigroup
• Span (linear algebra)
• Strict partial order
• Strict partial ordering
• Subgroup
• Symmetric group

T

• Tensor product of vector spaces
• The integers
• Topological group
• Transposition (group theory)
• Trivial
• Trivial (group)
• Trivial group

U

• U-ring
• Unity (ring)

V

• Vector space of linear maps between spaces
• Vector spaces