Category:Abstract algebra

A

• [+] Algebraic combinatorics (0)
• [+] Algebraic geometry (13)
• [+] Algebraic logic (0)
• [+] Algebraic number theory (4)
• [+] Algebraic structures (4)
• [+] Algebraic topology (13)

B

• [+] Binary operations (2)
• [+] Boolean algebra (1)

C

• [+] Commutative algebra (1)

D

• [+] Diagram algebras (0)
• [+] Differential algebra (0)

F

• [+] Field theory (4)

G

• [+] Galois theory (0)
• [+] Group theory (22)

H

• [+] Homological algebra (6)
• [+] Hypercomplex numbers (2)

I

• [+] Isomorphism theorems (0)

L

• [+] Lattice theory (2)
• [+] Localization (mathematics) (0)

M

• [+] Morphisms (2)

P

• [+] Process calculi (0)

R

• [+] Relational algebra (0)
• [+] Representation theory (6)
• [+] Ring theory (5)

S

• [+] Semigroup theory (1)

• List of abstract algebra topics
• Abstract algebra

A

• Absolute value (algebra)
• Absolutely convex set
• Absorption law
• Addition of natural numbers/Proofs
• Additive identity
• Additive inverse
• Affine Hecke algebra
• Algebraic K-theory
• Algebraic independence
• Algebraic number
• Algebraic number field
• Algebraic structure
• Algebraic topology
• Algebraically closed field
• Algebraically compact module
• Alternativity
• Anticommutativity
• Antihomomorphism
• Antiisomorphism
• Arity
• Artinian ideal
• Associativity
• A∞-operad

B

• BCK algebra
• Band (algebra)
• Bifundamental representation
• Binary function
• Binary operation
• Biquandle

C

• C-semiring
• Cancellative semigroup
• Canonical basis
• Casus irreducibilis
• Cauchy sequence
• Center (algebra)
• Chief series
• Closure with a twist
• Coimage
• Cokernel
• Commutativity
• Commutator
• Complement (set theory)
• Completely regular semigroup
• Composition ring
• Concatenation (mathematics)
• Conditional event algebra
• Cross product
• Cycle graph (algebra)
• Cyclic permutation

D

• Derivative algebra (abstract algebra)
• Differential graded algebra
• Dimension
• Dimension theorem for vector spaces
• Direct limit
• Direct product
• Distributivity

D cont.

• Dual basis in a field extension

E

• Eigenvalue, eigenvector and eigenspace
• Embedding
• Empty semigroup
• Esquisse d'un Programme
• Euclidean vector
• Expression (mathematics)
• External (mathematics)
• E∞-operad

F

• Formal derivative
• Formal power series
• Free object
• Fundamental theorem of algebra
• Fundamental theorem on homomorphisms

G

• Garside element
• General linear group
• Generating set
• Goddard–Thorn theorem
• Goodman-Nguyen-van Fraassen algebra
• Grothendieck group
• Group (mathematics)
• Group extension
• Groupoid

H

• Harmonic polynomial
• Heap (mathematics)
• Hecke algebra
• Seifert–van Kampen theorem
• Higher-dimensional algebra
• Hilbert–Poincaré series
• Homological algebra
• Homomorphic secret sharing
• Hyperstructure

I

• Icosian Calculus
• Idempotence
• Identity element
• Identity matrix
• Information algebra
• Interior algebra
• Intersection (set theory)
• Inverse element
• Inverse limit
• Inverse semigroup
• Involution (mathematics)
• Irreducible polynomial
• Isomorphism
• Isomorphism class
• Iterated binary operation

K

• Kernel (set theory)
• Krohn–Rhodes theory

L

• Latimer-MacDuffee theorem
• Lattice theorem
• Leibniz formula for determinants
• Light's associativity test
• Linear combination
• Linear independence
• Linear map
• Linear span
• List of Boolean algebra topics
• List of algebraic structures

L cont.

• List of group theory topics

M

• Magma (algebra)
• Matrix (mathematics)
• Matrix ring
• Module (mathematics)
• Monogenic semigroup
• Monoid
• Multiplicative group
• Multiplicative inverse

N

• Near-field (mathematics)
• Near-semiring
• Nearring
• List of publications by Emmy Noether
• Normal basis
• Normal extension
• Nowhere commutative semigroup
• Null semigroup

O

• Operad theory
• Operation (mathematics)
• Order of operations
• Ordered exponential
• Orthogonality

P

• Permutation
• Planar ternary ring
• Pointed set
• Polarization identity
• Polarization of an algebraic form
• Polynomial
• Polynomial expression
• Power set
• Predual
• Principle of distributivity
• Problems in loop theory and quasigroup theory
• Pseudogroup

Q

• Quincunx matrix
• Quotient module

R

• Racks and quandles
• Radical polynomial
• Rees factor semigroup
• Restriction of scalars
• Rng (algebra)
• Row and column spaces
• Rupture field

S

• Scalar (mathematics)
• Scalar multiplication
• Self-adjoint
• Semifield
• Semigroup with involution
• Semigroup with two elements
• Semigroupoid
• Semiprimitive ring
• Semiring
• Sequential dynamical system
• Setoid
• Simple (abstract algebra)
• Special classes of semigroups
• Special linear group
• Subquotient