﻿ 超Rpp半群的核心 Cores of Super Rpp Semigroups

Pure Mathematics
Vol.06 No.03(2016), Article ID:17524,5 pages
10.12677/PM.2016.63026

Cores of Super Rpp Semigroups

Huoping Ye, Junying Guo, Xiaojiang Guo

College of Mathematics and Information, Jiangxi Normal University, Nanchang Jiangxi

Received: Apr. 25th, 2016; accepted: May 9th, 2016; published: May 12th, 2016

Copyright © 2016 by authors and Hans Publishers Inc.

ABSTRACT

In this note, central (overabelian) super rpp semigroup is defined. These semigroups are generalization of the related classes of completely regular semigroups in the range of super rpp semi- groups. Some characterizations of such semigroups are obtained.

Keywords:Super Rpp Semigroup, Completely -Simple Semigroup

1. 引言和准备

。定义

(1)为幂等元当且仅当

(2) (的所有正则元组成的集合)，且构成的子半群；

(3)

(4)当且仅当

2. 主要结论

，于是的幂等元。而，现在，进而，这样的幂等元。故，再据

(1)

(2) 对于任意的(的幂等元集)，

(1)是中心的；

(2) 对于任意的是中心的；

(3) 对于任意的包含在的中心内，此处为包含幂等元-类。

(4)满足恒等式：

，则。由于为右同余，有

，且，则。据( [7] , Lemma II . 4.4, p. 75)，知

。注意到，的所有正则元构成完全单半群。易知，

。从而

Cores of Super Rpp Semigroups[J]. 理论数学, 2016, 06(03): 172-176. http://dx.doi.org/10.12677/PM.2016.63026

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