本原可分rpp半群  

Primitively Decomposable rpp Semigroups

作　　者：邱小伟 郭小江[1] 王军旗 吴瑕 Xiaowei Qiu;Xiaojiang Guo;Junqi Wang;Xia Wu(Department of Mathematics,Jiangxi Normal University,Nanchang)

机构地区：[1]江西师范大学数学与信息科学学院,南昌

出　　处：《理论数学》2012年第4期256-262,共7页Pure Mathematics

基　　金：国家自然科学基金(10961014);江西省自然科学基金(2014BAB201009);江西省教育厅科研项目助资(GJJ11388)。

摘　　要：完全0-单半群是一类非常重要的正则半群,也是正则半群结构基础。本原可分rpp半群是完全0-单半群在rpp半群理论中推广。本文主要研究本原可分rpp半群,给出了这类半群的若干特征,并证明了:半群为本原可分rpp半群当且仅当它是满足一些条件的左消幺半群上的Rees矩阵半群的同态像。此外,还研究了若干特类。Completely 0-simple semigroup is a very important class of regular semigroups, and it’s also the basis for the structure of regular semigroups. Primitively decomposable rpp semigroups are generalizations of completely 0-simple semigroups in the range of rpp semigroups. In this paper, the author studied primitively decomposable rpp semigroups, gave some characterizations for these semigroups and proved that a semigroup S was primitively decomposable rpp semigroup if and only if it was a homomorphic image of Rees matrix semigroup over a left cancellative monoid satisfying some conditions. In addition, some special primitively decomposable rpp semigroups were considered and discussed.

关 键 词：本原可分 RPP半群 REES矩阵半群 

分 类 号：O1[理学—数学]