III-homomorphisms and III-congruences on posets
type: Item
instance of: scholarly article
title: III-homomorphisms and III-congruences on posets
zbMATH Open document ID: 1148.06001
author: Pingyu Zhu
author: K. P. Shum
author: Niovi Kehayopulu
published in: Discrete Mathematics
publication date: 2008-10-07T00:00:00Z
review text: In the paper a new kind of homomorphism (III-homomorphism) between partially ordered sets is introduced and investigated. The authors study some properties of these homomorphisms, the corresponding congruences and their relationship to the other known homomorphisms, namely isotone mappings, strong homomorphisms, \(w\)-stable strong homomorphisms and \(LU\)-morphisms. III-homomorphisms turn out to be intermediate between strong homomorphisms and \(w\)-stable strong homomorphisms [\textit{R. Halaš}, ``Congruences on posets'', in: D. Dorninger et al. (eds.), Contributions to general algebra 12. Proceedings of the 58th workshop on general algebra ``58. Arbeitstagung Allgemeine Algebra'', Vienna, Austria, June 3--6, 1999. Klagenfurt: Verlag Johannes Heyn. 195--210 (2000; Zbl 0965.06001)]. The paper presents an approach which in some sense completes the hierarchy of definitions used so far.
reviewed by: Radomír Halaš
Mathematics Subject Classification ID: 06A06
Mathematics Subject Classification ID: 06B10
zbMATH DE Number: 5349300
zbMATH Keywords: isotone mapping
zbMATH Keywords: strong homomorphism
zbMATH Keywords: III-homomorphism
zbMATH Keywords: III-congruence
zbMATH Keywords: semilattice
MaRDI profile type: Publication
full work available at URL: j.disc.2007.10.038
OpenAlex ID: W2020188183
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DOI: 10.1016/J.DISC.2007.10.038
description: scientific article; zbMATH DE number 5349300