Difference between revisions of "Category:Abstract Algebra"

A

• ► Abstract Algebra Definitions‎ (4 C, 117 P)
• ► Abstract Algebra Examples‎ (1 C, 1 P)
• ► Abstract Algebra Theorems‎ (2 C, 21 P)

A cont.

• ► Abstract Algebra Theorems, lemmas and corollaries‎ (1 C, 22 P)

G

• ► Group Theory‎ (3 C, 30 P)

M

• ► Module Theory‎ (3 C, 19 P)

O

• ► Order Theory‎ (3 C, 25 P)

R

• ► Ring Theory‎ (4 C, 17 P)

T

• ► Types of rings‎ (1 P)

A

• A linear map is injective if and only if its kernel is trivial
• A linear map is injective if and only if the kernel contains only the zero vector
• Abelian group
• Absolute value (object)
• Abstract Algebra
• Abstract Algebra (subject)
• Template:Abstract algebra navbox
• Additive function
• An injective group homomorphism means the group is isomorphic to its image
• Associative

B

• Basis (linear algebra)
• Basis for the tensor product

C

• C-ring
• Canonical linear map
• Canonical projection of an equivalence relation
• Canonical projection of the equivalence relation
• Cartesian product
• Characteristic of a ring
• Characteristic property of the direct product module
• Characteristic property of the direct sum module
• Characteristic property of the tensor product
• Characteristic property of the tensor product/Statement
• 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 classes are either equal or disjoint
• Equivalence relation
• Notes:Equivalence relations
• Equivalence relations
• Examples of rings
• External direct sum module
• External direct sum of modules

F

• Factoring a function through the projection of an equivalence relation induced by that function yields an injection
• Field
• First group isomorphism theorem
• For a vector subspace of a topological vector space if there exists a non-empty open set contained in the subspace then the spaces are equal
• Formal linear combination

F cont.

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

G

• Generated subgroup
• Generator
• Geometrically independent set
• Group
• Group action
• Group factorisation theorem
• Group homomorphism
• Group homomorphism theorem
• Group Theory (subject)
• Template:Group theory navbox
• 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 Algebra (subject)
• Template:Linear algebra navbox
• Linear functional
• Linear functionals
• Linear maps

M

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

N

• Normal subgroup

O

• Ordered integral domain
• Ordered pairs
• Orthogonal vectors
• Overview of the group isomorphism theorems

P

• Partial order
• Partial ordering

P cont.

• Partition
• Partition (abstract algebra)
• Passing-to-the-quotient (function)
• Permutation
• Permutation of a set
• Permutation on a set
• Polynomial u-ring
• Poset
• Preorder
• Preordering
• Preset
• Products and coproducts of groups
• Notes:Products and sums of groups
• Notes:Proof of the first group isomorphism theorem
• Proof that the symmetric group is actually a group

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 dual space to the dual space of a vector space is canonically isomorphic to the vector space
• 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