Explore: Semigroup Rings

In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative internal binary operation on it. The binary operation

an I-semigroup and a *-semigroup. A class of semigroups important in semigroup theory are completely regular semigroups; these are I-semigroups in which

(Rev. 3rd ed.). New York: Springer-Verlag. ISBN 0-387-95385-X. R.Gilmer. Commutative semigroup rings. University of Chicago Press, Chicago–London, 1984

Commutative semigroup rings, University of Chicago Press, 1984, p. 172. Ali, Majid M.; Smith, David J. (2003), "Generalized GCD rings. II", Beiträge

quadratic integer rings. Quaternions, split-complex numbers, dual numbers, and possibly other hypercomplex number systems form *-rings (with their built-in

additive topological group and a multiplicative topological semigroup. Topological rings are fundamentally related to topological fields and arise naturally

apply to semigroups. In ring theory, the centralizer of a subset of a ring is defined with respect to the multiplication of the ring (a semigroup operation)

include the ring of n × n real square matrices with n ≥ 2, group rings in representation theory, operator algebras in functional analysis, rings of differential

called a (right) near-ring if: N is a group (not necessarily abelian) under addition; multiplication is associative (so N is a semigroup under multiplication);

computer science, an action or act of a semigroup on a set is a rule which associates to each element of the semigroup a transformation of the set in such