Abstract algebra is the field of mathematics concerned with the study of algebraic structures such as groups, rings and fields. The term "abstract algebra" is used to distinguish the field from "elementary algebra" or "high school algebra" which teaches the correct rules for manipulating formulas and algebraic expressions involving real and complex numbers.

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Subcategories

There are 14 subcategories to this category.

Algebraic geometry Algebraic number theory Algebraic topology B Boolean algebra

C Commutative algebra Computer algebra D Differential algebra G Group theory H Homological algebra

L Lie algebras Linear algebra M Module theory R Ring theory S Semigroup theory

Articles in category "Abstract algebra"

There are 186 articles in this category.

(0,1)-matrix A Abelian group Absorption law Abstract algebra Additive group Additive inverse Additive polynomial Algebra representation of a Hopf algebra Algebra representation of a Lie superalgebra Algebraic K-theory Algebraic extension Algebraic number Algebraic number field Algebraic structure Algebraic topology Algebraically closed field Algebraically compact module Algebraically independent Alternative algebra Alternativity Anticommutative Antihomomorphism Arity Artinian Artinian module Associativity Associator Automorphism B Basis (linear algebra) Bialgebra Bifundamental representation Bimodule Binary function Binary operation Biproduct C C-semiring Cancellation property Cayley's theorem Cayley-Dickson construction Center (algebra) Coalgebra Coimage Cokernel Commutative operation Commutator Comodule Coquaternion Cross product Crystal (mathematics) Cycle graph (group) Cyclic permutation D Derivative algebra (abstract algebra) Determinant Dimension Dimension theorem for vector spaces Direct limit Direct product Distributivity Domain (ring theory) Dot product Dual basis in a field extension Dual space

E Eigenvector Elementary symmetric polynomial Embedding Empty set Endomorphism Epimorphism Equaliser Euclidean domain Expression (mathematics) Extension (algebra) F Flat map Formal power series Free algebra Free module Free object Fundamental theorem of algebra Fundamental theorem on homomorphisms G General linear group Generating set Goddard-Thorn theorem Graded algebra Griess algebra Grothendieck group Group (mathematics) Group action Group generators Group theory Groupoid H Homological algebra Homomorphism Hopf algebra Hyperbolic quaternion Hyperbolic-orthogonal I Idempotent Identity element Identity matrix Integral closure Interior algebra Intersection (set theory) Inverse element Inverse limit Involution Irreducible polynomial Isomorphism J Jacobi identity Jordan algebra K Kernel of a function Killing spinor L Lie ring Linear algebra Linear combination Linear independence Linear span Linear transformation List of Boolean algebra topics List of abstract algebra topics List of group theory topics Locally cyclic group M Magma (algebra) Matrix (mathematics) Matrix ring Medial Monadic Boolean algebra

M cont. Monoid Monomorphism Multiplicative group Multiplicative inverse N Nearring Noetherian Nonassociative ring Normal basis O Octonion Order of operations Ordered exponential Ordered group Ordered ring Orthogonality P Pairing Permutation Permutation group Poisson algebra Poisson superalgebra Polynomial Power associativity Power set Predual Principle of distributivity Pseudogroup Pseudoscalar Q Quandle (knot theory) Quasigroup Quaternion Quaternions and spatial rotation Quillen-Suslin theorem R Rank (linear algebra) Representation of a Hopf algebra Restricted representation Ring (mathematics) Ring theory Row and column spaces S Scalar Scalar multiplication Sedenion Self-adjoint Semigroup Semigroupoid Semiprimitive ring Semiring Simple algebra Skolem hull Solvable Spectrum of a ring Spinor Split-complex number Splitting field Star-algebra Subfield (mathematics) Subquotient Subring Subsemigroup Swan's theorem Symmetric algebra Symmetric difference Symmetric polynomial