Primitively Decomposable rpp Semigroups
小伟 邱 · Pure Mathematics · 2012
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.