An infinite order operator on the lattice of varieties of completely regular semigroups
type: Item
instance of: scholarly article
title: An infinite order operator on the lattice of varieties of completely regular semigroups
zbMATH Open document ID: 0860.20045
DOI: 10.1007/BF01243591
author: Shuhua Zhang
published in: Algebra Universalis
publication date: 1996-10-22T00:00:00Z
review text: This paper is a continuation of the author's paper [in Semigroup Forum 48, No. 2, 180-192 (1994; Zbl 0797.20048)]. A completely regular semigroup is a union of groups. For a completely regular semigroup \(S\) let \(C^*(S)\) be the least full and self-conjugate subsemigroup of \(S\). Let \(A\) be a variety of completely regular semigroups and let \(AC^*\) be the class of all completely regular semigroups \(S\) such that \(C^*(S)\in A\). Then \(C^*\) is an operator on the lattice \(L\) of all varieties of completely regular semigroups. In the paper this operator \(C^*\) is studied. It is shown, that \(C^*\) is infinite. This yields that the Mal'cev product is not associative on \(L\). Several other lattice theoretic properties of \(C^*\) are investigated.
Mathematics Subject Classification ID: 20M07
Mathematics Subject Classification ID: 08B15
Mathematics Subject Classification ID: 20M17
zbMATH DE Number: 920792
zbMATH Keywords: lattices of varieties
zbMATH Keywords: unions of groups
zbMATH Keywords: varieties of completely regular semigroups
zbMATH Keywords: Mal'cev product
reviewed by: Vladimir Fleischer
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 920792