Minimal orthomodular lattices
type: Item
instance of: scholarly article
title: Minimal orthomodular lattices
zbMATH Open document ID: 0839.06006
DOI: 10.1007/BF00676237
published in: International Journal of Theoretical Physics
publication date: 1996-06-19T00:00:00Z
review text: For two classes of algebras \(C_2\subseteq C_1\) (minimal) exclusion systems \(\Sigma\subseteq C_1- C_2\) are discussed, for \(C_1\): all orthomodular lattices OML, \(C_2\): all modular ortholattices. A negative answer is given to the question of a finite \(\Sigma\) consisting of finite OML: Every such \(\Sigma\) contains an infinite OML. A minimal OML is a finite nonmodular OML with all proper sub-OML being modular. A characterization of these minimal OML \(T\) is given. Consider the irreducible \(T\) and the equational classes \([T]\) generated by \(T\): Every \([T]\) covers some \([\text{MO}_n]\), \(n\geq 2\), and for fixed \(n\) only finitely many such classes \([T]\) cover \([\text{MO}_n]\). Two such classes \([T]\), \([T']\) are incomparable whenever \(T\), \(T'\) are nonisomorphic.
Mathematics Subject Classification ID: 06C15
zbMATH DE Number: 844052
zbMATH Keywords: exclusion systems
zbMATH Keywords: orthomodular lattices
zbMATH Keywords: modular ortholattices
author: Jean Claude Carrega
reviewed by: Gudrun Kalmbach
MaRDI profile type: Publication
cites work: Q5841991
cites work: Varieties of Orthomodular Lattices. II
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cites work: Q3041254
cites work: Direct decompositions of orthomodular lattices
cites work: Algebras Whose Congruence Lattices are Distributive.
cites work: Q4750696
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description: scientific article; zbMATH DE number 844052