﻿ 关于完全π-正则半群分块定义的一个注记 A Note on the Definitions of Blocks of Epigroups

Pure Mathematics
Vol.06 No.02(2016), Article ID:17140,6 pages
10.12677/PM.2016.62013

A Note on the Definitions of Blocks of Epigroups

Qinqin Chen, Jingguo Liu*

School of Sciences, Linyi University, Linyi Shandong

Received: Feb. 28th, 2016; accepted: Mar. 9th, 2016; published: Mar. 16th, 2016

ABSTRACT

A semigroup is called an epigroup if for any element in this semigroup some power of the element lies in the maximal subgroup of the given semigroup. In this paper two variants of definitions of blocks of semigroups are given and we prove that two of them turn out to coincide in the case of epigroups. We also offer the third definition of blocks of epigroups and show that if blocks of epigroups are subsemigroups, then this definition is equivalent to the other two.

Keywords:Epigroup, Block, Regular-Class

1. 引言与预备知识

(i)

(ii) 对，若，则

(iii) 对，若，则

(i) T的非零-类为s的包含于D的非零-类；

(ii) T的非零-类为s的包含于D的非零-类；

(iii) T为完全0-单半群。

2. 分块的两个定义及等价性证明

2.1. 分块的两个定义

(i) 对任意

(ii) 对任意

(iii) 对任意

Moura(见文献 [14] )也给出了有限半群S的分块的定义。下面我们叙述该定义，并且去掉该文献中有限半群条件的限制，推广到一般半群上。

2.2. 定义2.1和定义2.2的等价性的证明

3. 分块为半群的情形

D的最大子集。则

A Note on the Definitions of Blocks of Epigroups[J]. 理论数学, 2016, 06(02): 89-94. http://dx.doi.org/10.12677/PM.2016.62013

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