Hyperidentities for some varieties of semigroups
type: Item
instance of: scholarly article
title: Hyperidentities for some varieties of semigroups
zbMATH Open document ID: 0692.08008
DOI: 10.1007/BF01190257
author: Shelly L. Wismath
published in: Algebra Universalis
publication date: 1990-01-01T00:00:00Z
review text: For a variety V of semigroups, \(\bar V\) denotes the largest variety of semigroups containing V and generating the same hypervariety (in the sense of W. Taylor) as V. If \(V=\bar V\) then V is called closed. The closure \(\bar V\) is found for any variety V of bands and also for any nilpotent variety \(V=N_ k\) (determined by \(x_ 1...x_ k=y_ 1...y_ k)\). For a nontrivial closed variety V of bands and any k, the join \(V\vee N_ k\) is proved to be also closed.
Mathematics Subject Classification ID: 08B05
Mathematics Subject Classification ID: 20M07
zbMATH DE Number: 4132234
zbMATH Keywords: variety of semigroups
zbMATH Keywords: hypervariety
zbMATH Keywords: closure
zbMATH Keywords: bands
zbMATH Keywords: nilpotent variety
zbMATH Keywords: closed variety
reviewed by: Jaroslav Ježek
MaRDI profile type: Publication
cites work: All varieties of bands
cites work: The lattice of equational classes of idempotent semigroups
cites work: Hyperidentities and hypervarieties
cites work: Q5758382
description: scientific article; zbMATH DE number 4132234