Category:Abstract algebra

• Abstract algebra
• List of abstract algebra topics

A

• A∞-operad
• Absolute value (algebra)
• Absolutely convex set
• Absorption law
• Proofs involving the addition of natural numbers
• Additive identity
• Additive inverse
• Algebraic element
• Algebraic independence
• Algebraic structure
• Algorithmic transparency
• Alternativity
• Anticommutativity
• Antidistributive
• Arity
• Associative property
• Automorphism

B

• Bendixson's inequality
• Bilinear form

C

• Canonical basis
• Casus irreducibilis
• Cauchy sequence
• Center (algebra)
• Centralizer and normalizer
• Closure (mathematics)
• Closure with a twist
• Coimage
• Cokernel
• Commutative property
• Commutator
• Conditional event algebra
• Cover (algebra)
• Cycle graph (algebra)
• Cyclic vector
• Cylinder (algebra)

D

• Dimension
• Direct limit
• Direct product
• Direct sum
• Distributive property
• Dixmier conjecture

E

• E∞-operad
• Eigenvalues and eigenvectors
• Embedding
• Euclidean vector
• Expression (mathematics)
• External (mathematics)

F

• Field (mathematics)
• Formal derivative
• Formal power series
• Free object

G

• Garside element
• General linear group
• Generating set of a module
• Generator (mathematics)
• Goodman–Nguyen–van Fraassen algebra
• Graded-commutative ring

H

• Harmonic polynomial
• Hasse–Schmidt derivation
• Hidden algebra
• Higher-order operad
• Homomorphic secret sharing
• Hyperstructure

I

• Icosian calculus
• Idealizer
• Idempotence
• Identity element
• Indeterminate (variable)
• Infinite expression
• Information algebra
• Interior algebra
• Inverse element
• Inverse limit
• Involution (mathematics)
• Irreducible polynomial
• Isomorphism class

K

• Kaplansky's theorem on projective modules
• Kernel (set theory)

L

• Left and right (algebra)
• Lie's theorem
• Light's associativity test
• Linear independence
• Linear map
• Linear span
• Locally finite operator
• Lulu smoothing

M

• Maximal common divisor
• Minimal ideal
• Multilinear form
• Multiplicative inverse

N

• N-ary associativity
• Near sets
• Near-ring
• Normal basis

O

• Operad
• Operad algebra
• Order of operations
• Ordered exponential
• Orthogonality

P

• Parallel (operator)
• Perfect complex
• Poincaré space
• Polarization identity
• Polarization of an algebraic form
• Power set
• Predual
• Principle of distributivity

R

• Radical polynomial
• Rational series
• Rayleigh's quotient in vibrations analysis
• Row and column spaces

S

• Scalar (mathematics)
• Scalar multiplication
• Self-adjoint
• Separating lattice homomorphism
• Sequential dynamical system
• Setoid
• Simple (abstract algebra)
• Skew-Hermitian matrix
• Split exact sequence
• Subquotient

T

• Total algebra
• Transpose

U

• Universal embedding theorem

W

• Wheel theory
• Word problem (mathematics)

Y

• Yoneda product

Z

• Zero divisor
• Zero-product property