Injective and projective regular double Stone algebras
type: Item
instance of: scholarly article
title: Injective and projective regular double Stone algebras
zbMATH Open document ID: 0648.06006
DOI: 10.1007/BF01195261
published in: Algebra Universalis
publication date: 1987-01-01T00:00:00Z
review text: A double Stone algebra \(L=(L;\vee,\wedge,\quad *,\quad +,0,1)\) is a bounded distributive lattice such that L and its dual \(\bar L\) are pseudocomplemented (i.e. \(x\leq a\) * iff \(x\wedge a=0\) and \(x\geq a\) \(+\) iff \(x\vee a=1)\) and it satisfies the identities x \(*\vee x^{**}=1\), x \(+\wedge x^{++}=0\). A double Stone algebra is called regular, if it satisfies the condition: x \(*=y\) * and x \(+=y\) \(+\) imply \(x=y\). This is a continuation of the author's paper in Houston J. Math. 9, 455-463 (1983; Zbl 0531.06007). The author gives a characterization of injective regular double Stone algebras [see also the reviewer's paper in Algebra Univ. 4, 259-267 (1974; Zbl 0302.06022)] and a characterization of projective regular double Stone algebras. In particular, he describes those regular double Stone algebras which are also projective in the category of double Stone algebras.
Mathematics Subject Classification ID: 06D15
Mathematics Subject Classification ID: 06D20
Mathematics Subject Classification ID: 08B30
Mathematics Subject Classification ID: 06D25
Mathematics Subject Classification ID: 06D30
zbMATH DE Number: 4057578
zbMATH Keywords: projective algebra
zbMATH Keywords: injective algebra
zbMATH Keywords: bounded distributive lattice
zbMATH Keywords: pseudocomplemented
zbMATH Keywords: regular double Stone algebras
Wikidata QID: Q114234029
author: Ivo Düntsch
reviewed by: Tibor Katriňák
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01195261
OpenAlex ID: W1994605172
description: scientific article; zbMATH DE number 4057578