具有弱正规幂等元的rpp半群的结构

The Structure of rpp Semigroups with a Weak Normal Idempotent

研究一类特殊的rpp半群,即含弱正规幂等元的rpp半群。作者首先给出了这类半群的若干特征,然后通过右正规带和具有某些相应性质的rpp半群建立了具有弱正规幂等元的rpp半群的结构。把郭小江在富足半群上得到的结果进行了很好的推广和发展。另外,(弱)正规幂等元与目前颇受重视的另一个概念-适当断面(adequate transversal)有着密切的联系。自然。

It is well known that the concept of rpp semigroups was initiated by Fountain in 1982. And follow Fountain, the class of rpp semigroups includes the class of abundant semigroups as a special subclass. In the reference, xiaojiang Guo defined and investigated weak medial idempotents and weak normal idempotents and established the structure of abundant with weak normal idempotents. The aim of this paper is to study special rpp semigroups, namely, rpp semigroups with weak normal idempotents. Some properties and characterizations for such semigroups are ob- tained. In particular,we establish the structure of this class of rpp semigroups in terms of right normal band and rpp semigroups with some simple compatibility. Result by Guo Xiaojiang on abundant semigroups are extended and strengthened.