含逆断面半群的等价刻划  

Some Conditions of Equivalence about Sem igroups with Inverse Transversals

作　　者：罗敏霞[1] 

机构地区：[1]运城学院应用数学系,山西运城044000

出　　处：《运城学院学报》2006年第2期1-3,共3页Journal of Yuncheng University

摘　　要：本文引入一种格林关系,0-格林关系,采用Lawson提出的研究正则半群的新的研究方法—整体逆扩张(en largem ent),对含逆断面半群进行研究,给出了含逆断面半群的等价刻划,证明了S0是S的一个逆断面当且仅当P={e∈S;(e′∈V(e)∩S0)ee′=e}中每个元素的R0-类只含一个幂等元,Q={f∈S;(f′∈V(f)∩S0)ff′=f}中每个元素的L0-类只含一个幂等元.In this paper, we introduce a Green relation which is 0 - Green relation. This paper studied semigroups with inverse transversals by a new research method--enlargement, which is about regular semigroups by Lawson. Some conditions of equivalence of semigroups with inverse transversals was given. We prove that S） is an inverse transversal of semigroup S if and only if each R^0 - class of P={e∈S;（Зe＇∈V（e）∩S^0）ee＇=e} contains an unique idempotent, and each L^0 - class of Q={f∈S;（Зf＇∈V（f）∩S^0）ff=f} contains an unique idempotent.

关 键 词：0-格林关系 逆断面 整体逆扩张 

分 类 号：O151.21[理学—数学]