On \(E_ k\)-semigroups
type: Item
instance of: scholarly article
title: On \(E_ k\)-semigroups
zbMATH Open document ID: 0623.20049
DOI: 10.1007/BF02573170
published in: Semigroup Forum
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/134846
review text: Let S be a semigroup and E the set of idempotents of S. Let k be a positive integer. If \(S\neq E\), \(| E| \geq k\) and every nonidempotent subsemigroup of S, containing k idempotents, contains the whole E, then S is said to be an \(E_ k\)-semigroup. If \(S\neq E\) and \(| E| =k\) then S is obviously an \(E_ k\)-semigroup which is called trivial. The authors study \(E_ k\)-semigroups for \(k=1,2\). It is shown that there are no nontrivial \(E_ 1\)-semigroups. A characterization of nontrivial \(E_ 2\)-semigroups is given which is used for obtaining a stucture theorem for these semigroups.
Mathematics Subject Classification ID: 20M10
zbMATH DE Number: 4010792
zbMATH Keywords: idempotents
zbMATH Keywords: \(E_ k\)-semigroups
author: A. Cherubini
author: Ada Varisco
reviewed by: S. M. Goberstein
MaRDI profile type: Publication
cites work: Q4172233
cites work: On Putcha's Q-semigroups
cites work: On $E_k$-rings
cites work: Q3848243
cites work: Q4083905
cites work: Q4123538
OpenAlex ID: W2325924410
description: scientific article; zbMATH DE number 4010792