理论数学  >> Vol. 2 No. 4 (October 2012)

本原可分rpp半群
Primitively Decomposable rpp Semigroups

DOI: 10.12677/PM.2012.24039, PDF, HTML,  被引量 下载: 2,767  浏览: 7,879  国家自然科学基金支持

作者: 邱小伟, 郭小江*, 王军旗*, 吴 瑕*:江西师范大学,数学与信息科学学院

关键词: 本原可分rpp半群Rees矩阵半群Primitively Decomposable; rpp Semigroups; Rees Matrix Semigroups

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。
Abstract: Completely 0-simple semigroup is a very important class of regular semigroups, and its 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.

文章引用: 邱小伟, 郭小江, 王军旗, 吴瑕. 本原可分rpp半群[J]. 理论数学, 2012, 2(4): 256-262. http://dx.doi.org/10.12677/PM.2012.24039