A Structure of Quasi-C* Semigroups

Abstract

An abundant semigroup is called a quasi-C* semigroup if xeyz=xyez for any x,y,z in S and e in E(S). In this article, we studied the structure of quasi-C* semigroups. By using the quasi-direct product, we prove that a semigroup S is a quasi-C* semigroup if and only if S is a quasi-direct product of a left normal band, a C-a semigroup and a right normal band. This result generalizes C-a semigroups.