On varieties of modular ortholattices that are generated by their finite-dimensional members.
type: Item
instance of: scholarly article
title: On varieties of modular ortholattices that are generated by their finite-dimensional members.
zbMATH Open document ID: 1306.06006
author: Christian Herrmann
author: Micheale Susan Roddy
published in: Algebra Universalis
publication date: 2015-01-09T00:00:00Z
review text: A modular ortholattice is an algebra \((L,\vee,\wedge,',0,1)\) of type \((2,2,1,0,0)\) such that \((L,\vee,\wedge,0,1)\) is a bounded modular lattice and the identities \(x\vee x'=1\), \(x\wedge x'=0\), \((x')'=x\), \((x\vee y)'=x'\wedge y'\) and \((x\wedge y)'=x'\vee y'\) hold. Let \(\mathcal L\) be a modular ortholattice and \(\mathcal V\) a variety of modular ortholattices. The dimension of \(\mathcal L\) is the cardinality of a maximal chain in \(\mathcal L\) minus one. The fact that \(\mathcal L\) belongs to the variety generated by the finite-dimensional members of \(\mathcal V\) is characterized in two different ways.
reviewed by: Helmut Länger
Mathematics Subject Classification ID: 06C15
Mathematics Subject Classification ID: 06C20
Mathematics Subject Classification ID: 08B15
Mathematics Subject Classification ID: 51A50
zbMATH DE Number: 6384896
zbMATH Keywords: varieties of modular ortholattices
zbMATH Keywords: dimension modular ortholattices
zbMATH Keywords: finite-dimensional modular ortholattices
zbMATH Keywords: maximal chains
MaRDI profile type: Publication
full work available at URL: s00012-014-0305-0
OpenAlex ID: W2017243423
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DOI: 10.1007/S00012-014-0305-0
description: scientific article; zbMATH DE number 6384896