本原可分rpp半群
Primitively Decomposable rpp Semigroups

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 (2012) 本原可分rpp半群。 理论数学, 2, 256-262. doi: 10.12677/PM.2012.24039

参考文献

[1] K. S. S. Nambooripad. Structure of regular semigroups II. Semigroup Forum, 1975, 9: 364-371.

[2] K. S. S. Nambooripad. Structure of regular semigroups I. American Mathematical Society, 1979, 22(224): vii+119.

[3] O. Steinfeld. On a generalization of completely 0-simple semigroups. Acta Scientia Mathematica (Szeged), 1967, 28: 135-145.

[4] J. B. Fountain. Abundant semigroups. Proceedings London Mathematical Society, 1982, 44(3): 103-129.

[5] J. M. Howie. An introduction to semigroup theory. London: Academic Press, 1976.

[6] J. B. Fountain. Adequate semigroups. Proceedings of Edinburgh Mathematical Society, 1979, 22(2): 113-125.

分享
Top