A Structure of Regular Semigroups With a Regular *-transversal
LI Yong-hua · Advances in Mathematics · 2006
Let S be a regular semigroup.If there are a subsemigroup S~* of S and a unary operation * in S satisfying:(1)x~*∈S~*∩V(x)for any x∈S;(2)(x~*)~*=x for any x∈S~*;(3)(x~*y)~*=y~*x~(**)and (xy~*)~*=y~(**)x~* for any x,y∈S,then we say that S~* is a regular *-transversal of S.In this paper we describe a general structure of regular semigroups with a regular *-transversal.