Orthocomplemented lattices with a symmetric difference
type: Item
instance of: scholarly article
title: Orthocomplemented lattices with a symmetric difference
zbMATH Open document ID: 1186.06004
author: Milan Matoušek
published in: Algebra Universalis
publication date: 2010-01-04T00:00:00Z
review text: The central notion of this paper is the so-called orthocomplemented difference lattice (shortly ODL). This is an ortholattice endowed with an additional binary operation (the so-called symmetric difference) satisfying certain axioms. Every ODL induces a corresponding orthomodular lattice. Valuations, set-representable ODLs (shortly SRODLs), several types of ideals as well as horizontal sums of Boolean algebras are considered. SRODLs are characterized by means of the existence of certain valuations respectively ideals and it is shown that the class of all SRODLs forms a variety. Examples of ODLs being not set-representable are given.
reviewed by: Helmut Länger
Mathematics Subject Classification ID: 06C15
Mathematics Subject Classification ID: 03G12
zbMATH DE Number: 5652277
zbMATH Keywords: orthocomplemented difference lattice
zbMATH Keywords: ortholattice
zbMATH Keywords: symmetric difference
zbMATH Keywords: orthomodular lattice
zbMATH Keywords: evaluation
zbMATH Keywords: set-representable
zbMATH Keywords: ideal
zbMATH Keywords: horizontal sum
zbMATH Keywords: Boolean algebra
zbMATH Keywords: variety
MaRDI profile type: Publication
full work available at URL: s00012-009-2105-5
OpenAlex ID: W2069664407
DOI: 10.1007/S00012-009-2105-5
description: scientific article; zbMATH DE number 5652277