The intersection of pseudovarieties of central simple semigroups.
type: Item
instance of: scholarly article
title: The intersection of pseudovarieties of central simple semigroups.
zbMATH Open document ID: 1115.20046
author: Edmond W. H. Lee
author: Norman R. Reilly
published in: Semigroup Forum
publication date: 2007-01-24T00:00:00Z
review text: Given two pseudovarieties \(P_S(A)\) and \(P_S(B)\) that are generated by finite semigroups \(A\) and \(B\), respectively, it is in general very difficult to determine whether or not the intersection \(P_S(A)\cap P_S(B)\) is a pseudovariety generated by a finite semigroup. The authors consider the following Kublanovsky problem: find an operation \(\circ\) which given two finite simple semigroups \(A\) and \(B\) returns a finite simple semigroup \(A\circ B\) with \(P_S(A)\cap P_S(B)=P_S(A\circ B)\). They present a solution to this problem for finite central simple semigroups \(A\) and \(B\). (A completely simple semigroup \(S\) is called central if the product of any two idempotents of \(S\) lies in the center of the maximal subgroup containing it.) Moreover, the authors present several examples of critical semigroups, including an infinite class of critical monoids.
Mathematics Subject Classification ID: 20M07
Mathematics Subject Classification ID: 08B15
Mathematics Subject Classification ID: 08C15
zbMATH DE Number: 5118106
zbMATH Keywords: pseudovarieties of semigroups
zbMATH Keywords: central simple semigroups
zbMATH Keywords: critical semigroups
zbMATH Keywords: finite semigroups
zbMATH Keywords: idempotents
reviewed by: Leonid M. Martynov
MaRDI profile type: Publication
full work available at URL: s00233-006-0604-7
OpenAlex ID: W2024425953
DOI: 10.1007/S00233-006-0604-7
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description: scientific article; zbMATH DE number 5118106