The ideal retraction property for idempotent semigroups.
type: Item
instance of: scholarly article
title: The ideal retraction property for idempotent semigroups.
zbMATH Open document ID: 1123.20050
author: N. E. Zubov
published in: Semigroup Forum
publication date: 2007-05-03T00:00:00Z
review text: A semigroup \(S\) is said to have the `ideal retraction property' provided each of its ideals is the image of an idempotent endomorphism of \(S\). It is proved that a band \(B=[Y;S_\alpha]\) (presented as a semilattice of rectangular bands) has the ideal retraction property if and only if \(B\) is normal and \(Y\) is a tree that contains no \(\omega+1\) chain.
Mathematics Subject Classification ID: 20M10
Mathematics Subject Classification ID: 20M12
Mathematics Subject Classification ID: 06A12
Mathematics Subject Classification ID: 20M15
zbMATH DE Number: 5148908
zbMATH Keywords: normal bands
zbMATH Keywords: ideal retractions
zbMATH Keywords: idempotent endomorphisms
zbMATH Keywords: idempotent semigroups
zbMATH Keywords: semilattice homomorphic images
reviewed by: Peeter Normak
MaRDI profile type: Publication
full work available at URL: s00233-006-0664-8
OpenAlex ID: W2057058672
DOI: 10.1007/S00233-006-0664-8
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description: scientific article; zbMATH DE number 5148908