semigroup

1. (mathematics) Any set for which there is a binary operation that is closed and associative.Examples: "If a semigroup S contains a zeroid, then every left zeroid is also a right zeroid, and vice versa, and the set K of all the zeroids of S is the kernel of S."; "1988, A. Ya Aǐzenshtat, Boris M. Schein (translator), On Ideals of Semigroups of Endomorphisms, Ben Silver (editor), Nineteen Papers on Algebraic Semigroups, American Mathematical Society Translations, Series 2, Volume 139, page 11, It follows naturally that various classes of ordered sets can be characterized by semigroup properties of endomorphism semigroups."; "If one considers the variety of semigroups, one has the binary operation of multiplication defined on every semigroup."