Regular WE-2 semigroups
type: Item
instance of: scholarly article
title: Regular WE-2 semigroups
zbMATH Open document ID: 0606.20052
DOI: 10.1007/BF02573164
author: B. George
published in: Semigroup Forum
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/134840
review text: Let m be a positive integer greater than one. A semigroup is called an E- m semigroup if it satisfies the identity \((xy)^ m=x^ my^ m\). A WE-m semigroup is a semigroup S such that for every x,y\(\in S\), there exists a positive integer k such that \((xy)^{m+k}=x^ my^ m(xy)^ k=(xy)^ kx^ my^ m\). It is shown that the regular WE-2 semigroups are exactly the regular E-2 semigroups and that an ideal extension of a regular semigroup K by a nil semigroup N is a WE-2 semigroup iff K is an E-2 semigroup and the extension is a retract extension.
Mathematics Subject Classification ID: 20M10
zbMATH DE Number: 3979377
zbMATH Keywords: regular WE-2 semigroups
zbMATH Keywords: regular E-2 semigroups
zbMATH Keywords: ideal extension
zbMATH Keywords: nil semigroup
zbMATH Keywords: retract extension
reviewed by: S. M. Goberstein
MaRDI profile type: Publication
cites work: Q3848243
cites work: The structure of orthodox unions of groups
cites work: Weakly exponential semigroups
cites work: WE-m semigroups
cites work: Semigroups satisfying \((xy)^m=x^my^m\)
cites work: Q4148155
cites work: On exponential semigroups, I
Recommended article: Q4624837
Recommended article: WE-m semigroups
Recommended article: Q4926353
Recommended article: REGULAR SEMIHYPERGROUPS
Recommended article: Weaky regular \(*\)-semigroups
Recommended article: Q5209704
Recommended article: Q4894447
Recommended article: Q5004764
Recommended article: On weakly regular semi group
Recommended article: Q4438298
description: scientific article; zbMATH DE number 3979377