Geodesic
Orthomodular lattices with state-separated noncompatible pairs
Czechoslovak Mathematical Journal, Tome 50 (2000) no. 2, pp. 359-366 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In the logico-algebraic foundation of quantum mechanics one often deals with the orthomodular lattices (OML) which enjoy state-separating properties of noncompatible pairs (see e.g. , and ). These properties usually guarantee reasonable “richness” of the state space—an assumption needed in developing the theory of quantum logics. In this note we consider these classes of OMLs from the universal algebra standpoint, showing, as the main result, that these classes form quasivarieties. We also illustrate by examples that these classes may (and need not) be varieties. The results supplement the research carried on in , , , , , , , and .
In the logico-algebraic foundation of quantum mechanics one often deals with the orthomodular lattices (OML) which enjoy state-separating properties of noncompatible pairs (see e.g. , and ). These properties usually guarantee reasonable “richness” of the state space—an assumption needed in developing the theory of quantum logics. In this note we consider these classes of OMLs from the universal algebra standpoint, showing, as the main result, that these classes form quasivarieties. We also illustrate by examples that these classes may (and need not) be varieties. The results supplement the research carried on in , , , , , , , and .
Classification : 06C15, 08C15, 81P10
Keywords: orthomodular lattice; state; noncompatible pairs; (quasi)variety 
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     author = {Mayet, R. and Pt\'ak, P.},
     title = {Orthomodular lattices with state-separated noncompatible pairs},
     journal = {Czechoslovak Mathematical Journal},
     pages = {359--366},
     year = {2000},
     volume = {50},
     number = {2},
     mrnumber = {1761393},
     zbl = {1047.06005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2000_50_2_a10/}
}
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Mayet, R.; Pták, P. Orthomodular lattices with state-separated noncompatible pairs. Czechoslovak Mathematical Journal, Tome 50 (2000) no. 2, pp. 359-366. http://geodesic.mathdoc.fr/item/CMJ_2000_50_2_a10/