正则单半群的一个充要条件

A Necessary and Sufficient Condition for Simple Regular Semigroups

将逆半群为单半群的一个充要条件推广到正则半群,它把正则半群的单性转化为幂等元之间的偏序和GreenD关系,揭示了GreenD关系与理想概念之间的内在联系.最后给出了一个应用,并用一个例子说明正则性条件不可少.

In this paper, a necessary and sufficient condition for an inverse semigroup to be simple stated in paper (Howie J M. Fundamentals of Semigroup Theory.Oxford:Clarendon Press,1995.) is generalized to general regular semigroups. That is, a regular semigroup S is simple if and only if for any idempotents e,f∈S, there exists an idempotent g such that g≤f and gDe.An application is given. A counter example is also given to prove that the regularity condition in the theorem can not be dropped.