Algebraic structure

Summary

An algebraic structure, or algebra, is a set together with a family of finitary operations on it. The names and arities of the operations form a signature with no relation symbols, so an algebraic structure is a structure of a special kind. Groups, rings, fields, lattices and vector spaces are the main examples. A kind of algebraic structure is usually fixed by its signature and by a list of axioms, often identities, that the operations satisfy.