Dilworth's principal elements
type: Item
instance of: scholarly article
title: Dilworth's principal elements
zbMATH Open document ID: 0901.06013
DOI: 10.1007/BF01236764
author: E. W. Johnson
author: D. D. Anderson
published in: Algebra Universalis
publication date: 1998-11-24T00:00:00Z
review text: By \textit{R. P. Dilworth,} an element \(e\) of a multiplicative lattice is called principal if it satisfies the identifies \(a\wedge be=\big ((a:e)\wedge b\big)e\) and \(a\vee (b: e)=(ae\vee b):e.\) Principal elements in multiplicative lattices are the analogue of principal ideals in (commutative) rings. New results regarding principal elements are obtained in the paper; some earlier ones are extended. Applications to ring ideals are given. In addition, the paper contains a number of open problem and a fairly extensive bibliography on principal elements.
Mathematics Subject Classification ID: 06F10
Mathematics Subject Classification ID: 16P40
zbMATH DE Number: 1226551
zbMATH Keywords: multiplicative lattice
zbMATH Keywords: principal element
zbMATH Keywords: ring ideal
reviewed by: Jaromír Duda
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1226551