ON A PROBLEM OF M. KAMBITES REGARDING ABUNDANT SEMIGROUPS

被引：6

作者：

Araujo, Joao ^{[1
,2
]}

Kinyon, Michael ^{[3
]}

机构：

[1] Univ Aberta, Lisbon, Portugal

[2] Univ Lisbon, Ctr Algebra, P-1649003 Lisbon, Portugal

[3] Univ Denver, Dept Math, Denver, CO USA

来源：

COMMUNICATIONS IN ALGEBRA | 2012年 / 40卷 / 12期

关键词：

Abundant semigroups; Adequate semigroups; Amiable semigroups;

D O I：

10.1080/00927872.2011.610072

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A semigroup is regular if it contains at least one idempotent in each R-class and in each L-class. A regular semigroup is inverse if it satisfies either of the following equivalent conditions: (i) there is a unique idempotent in each R-class and in each L-class, or (ii) the idempotents commute. Analogously, a semigroup is abundant if it contains at least one idempotent in each R*-class and in each L*-class. An abundant semigroup is adequate if its idempotents commute. In adequate semigroups, there is a unique idempotent in each R* and L*-class. M. Kambites raised the question of the converse: in a finite abundant semigroup such that there is a unique idempotent in each R* and L*-class, must the idempotents commute? In this note, we provide a negative answer to this question.

引用

页码：4439 / 4447

页数：9