Uniform bands.
type: Item
instance of: scholarly article
zbMATH Open document ID: 1306.20062
DOI: 10.1017/S0013091513000709
author: Justin Albert
author: Francis Pastijn
publication date: 2014-09-30T00:00:00Z
Mathematics Subject Classification ID: 20M19
Mathematics Subject Classification ID: 20M07
Mathematics Subject Classification ID: 20M17
Mathematics Subject Classification ID: 20M18
zbMATH DE Number: 6349664
zbMATH Keywords: idempotent semigroups
zbMATH Keywords: uniform semilattices
zbMATH Keywords: uniform bands
zbMATH Keywords: orthodox semigroups
zbMATH Keywords: bisimple semigroups
zbMATH Keywords: varieties of semigroups
zbMATH Keywords: idempotents
zbMATH Keywords: embeddings
MaRDI profile type: Publication
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full work available at URL: s0013091513000709
OpenAlex ID: W4234113274
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title: Uniform bands.
published in: Proceedings of the Edinburgh Mathematical Society. Series II
review text: A band (idempotent semigroup) \(B\) is \textit{uniform} if \(eBe\cong fBf\) for all \(e,f\in B\). The second author [\textit{F. Pastijn}, Acta Sci. Math. 42, 305-311 (1980; Zbl 0467.06005)] showed that any semilattice can be embedded in a uniform semilattice. The construction used therein is generalized to show that any band can be embedded in a uniform band that generates the same variety as the original.NEWLINENEWLINE An \textit{orthodox} semigroup is a regular semigroup whose idempotents form a band. It is well known that a band is uniform if and only if it is the band of idempotents of some bisimple orthodox semigroup. It is also shown that any orthodox semigroup is embeddable into a bisimple orthodox semigroup, whose band of idempotents generates the same variety as that of the original. Moreover, except when the original semigroup is a rectangular group, the larger semigroup can be chosen to be fundamental.
reviewed by: Peter R. Jones
description: scientific article; zbMATH DE number 6349664