On \(n\)-normal posets
type: Item
instance of: scholarly article
title: On \(n\)-normal posets
zbMATH Open document ID: 1234.06003
author: Radomír Halaš
author: Vinayak Joshi
author: V. S. Kharat
published in: Central European Journal of Mathematics
publication date: 2011-05-27T00:00:00Z
review text: The authors introduce the notion of \(n\)-normality for partially ordered sets. Thus, a poset is said to be \(n\)-normal provided that every of its prime ideals contains at most \(n\) prime ideals. Matching this new concept and the prime ideal theorem for finite ideal distributive posets, the authors describe the main properties of \(n\)-normal posets, and characterize them among finite ideal-distributive posets thus generalizing a result by \textit{W. H. Cornish} [``\(n\)-normal lattices'', Proc. Am. Math. Soc. 45, 48--54 (1974; Zbl 0294.06008)].
Mathematics Subject Classification ID: 06A11
zbMATH DE Number: 5900624
zbMATH Keywords: \(n\)-normal poset
zbMATH Keywords: distributive poset
zbMATH Keywords: prime ideal
zbMATH Keywords: unique minimal prime ideal
zbMATH Keywords: polar
reviewed by: Esteban Induraín
MaRDI profile type: Publication
full work available at URL: s11533-010-0062-z
OpenAlex ID: W2062716651
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cites work: Characterizations of normal lattices
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DOI: 10.2478/S11533-010-0062-Z
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description: scientific article; zbMATH DE number 5900624