A Necessary and Sufficient Condition for Simple Regular Semigroups
Huang Xue-jun · Journal of Sichuan Normal University · 2005
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.