On maximal pseudo-varieties of finite monoids and semigroups
type: Item
instance of: scholarly article
title: On maximal pseudo-varieties of finite monoids and semigroups
zbMATH Open document ID: 0846.20062
author: S. W. Margolis
published in: Russian Mathematics
publication date: 1996-05-21T00:00:00Z
review text: The main result of the article states that there are no elements in the lattice of semigroup pseudo-varieties covered by the pseudo-variety of all finite semigroups. The author shows that a slight modification of the proof permits to obtain the analogous result for pseudo-varieties of monoids. He notes also that methods of the paper can be used to prove that some proper pseudo-varieties of semigroups do not have maximal subpseudo-varieties. This is proved explicitly for the pseudo-variety of all finite semigroups all whose subgroups are commutative. One can note that recently \textit{S. Margolis, M. Sapir} and \textit{P. Weil} have proved that each of the three pseudo-varieties mentioned above is not decomposable into the join of two proper subpseudo-varieties [Rapports LITP 96/01 (1996)]. Clearly, this implies the results of the paper under review.
Mathematics Subject Classification ID: 20M07
Mathematics Subject Classification ID: 08B15
Mathematics Subject Classification ID: 08C15
zbMATH DE Number: 862280
zbMATH Keywords: pseudo-variety of finite semigroups
zbMATH Keywords: lattice of semigroup pseudo-varieties
zbMATH Keywords: pseudo-varieties of monoids
zbMATH Keywords: pseudo-varieties of semigroups
reviewed by: Boris Vernikov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 862280