Learn and talk about Algebraic structures, Abstract algebra, Mathematical structures, Universal algebra

In algebra, a branch of pure mathematics, an algebraic structure consists of one or more sets closed under one or more operations, satisfying some axioms. Abstract algebra is primarily the study of algebraic structures and their properties. The notion of algebraic structure has been formalized in universal algebra.

Algebras	Coalgebras	Finite groups	Lie groups	Non-associative algebra
Ordered algebraic structures	Properties of groups

Action algebra	Algebraic structure	BCK algebra	Band (mathematics)	Biordered set
Biquandle	Boolean algebra (structure)	C-semiring	Cancellative semigroup	Clifford semigroup
Commutative ring	Complete Heyting algebra	Completely regular semigroup	Composition ring	Damm algorithm
Domain (ring theory)	Double groupoid	Empty semigroup	Essential dimension	Exponential field
Exponentially closed field	Field (mathematics)	Finite lattice representation problem	Finitely-generated abelian group	Grothendieck group
Group (mathematics)	Groupoid	Hardy field	Heap (mathematics)	Ideal (ring theory)
Infrastructure (number theory)	Inverse semigroup	Kasch ring	Kleene algebra	Lattice (order)
Lindenbaum–Tarski algebra	MV-algebra	Magma (algebra)	Matrix ring	Module (mathematics)
Monogenic semigroup	Monoid	Moufang polygon	Multiplicative group	N-ary group
Near-field (mathematics)	Near-semiring	Nowhere commutative semigroup	Numerical semigroup	Ockham algebra
Outline of algebraic structures	Planar ternary ring	Pregroup	Primitive ring	Pseudo-ring
Pseudogroup	Quantum differential calculus	Racks and quandles	Ring (mathematics)	Semifield
Semigroup	Semigroup with involution	Semigroup with two elements	Semigroupoid	Semilattice
Semiprimitive ring	Semiring	Special classes of semigroups	Symmetric inverse semigroup	Torsion-free abelian group
Trivial semigroup

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Algebraic structures