P－正则半群的双序集

Biordered Sets of P-regular Semigroups

本文刻划了双序集Ｅ为某Ｐ－正则半群的幂等元双序集的充要条件．所得定理不仅推广了Ｄ．Ｅａｓｄｏｗｎ关于带的双序集的结论，而且导出了正则＊－半群的幂等元双序集的一个刻划．进而还对Ｐ－正则半群的若干特殊情形及向非正则半群的推广进行了讨论．

The necessary and sufficient condition for a biordered set to be that of the idempotents of a P-regular semigroup is characterized in this paper.The theorem obtained here not only is a generalization of the theorem, given by D.Easdown,for biordered sets of bands,but also gives a characterization of biordered sets of idempotents of regular *-semigroups.Further,some special cases and a generalization to non-regular ones of P-regular semigroups are discussed.