具有正则*-断面的正则半群的结构

摘要

Let S be a regular semigroup. If there are a subsemigroup S* of S and aunary 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.%设S是一个正则半群.如果存在一个S的子半群S*及上的一元运算*满足条件:(1)(A)x∈S,x*∈S*∩V(x);(2)(A)x∈S*,(x*)*=x;(3)(A)x,y∈S,(x*y)*=y*x**,(xy*)*=y**x*则称S*是S的一个正则*-断面.本文刻画了具有正则*-断面的正则半群的结构.