Orthomodular lattices with state-separated noncompatible pairs

R. Mayet; Pavel Pták

Czechoslovak Mathematical Journal (2000)

  • Volume: 50, Issue: 2, page 359-366
  • ISSN: 0011-4642

Abstract

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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 .

How to cite

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Mayet, R., and Pták, Pavel. "Orthomodular lattices with state-separated noncompatible pairs." Czechoslovak Mathematical Journal 50.2 (2000): 359-366. <http://eudml.org/doc/30567>.

@article{Mayet2000,
abstract = {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 .},
author = {Mayet, R., Pták, Pavel},
journal = {Czechoslovak Mathematical Journal},
keywords = {orthomodular lattice; state; noncompatible pairs; (quasi)variety; orthomodular lattice; state; noncompatible pairs; (quasi)variety},
language = {eng},
number = {2},
pages = {359-366},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Orthomodular lattices with state-separated noncompatible pairs},
url = {http://eudml.org/doc/30567},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Mayet, R.
AU - Pták, Pavel
TI - Orthomodular lattices with state-separated noncompatible pairs
JO - Czechoslovak Mathematical Journal
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 50
IS - 2
SP - 359
EP - 366
AB - 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 .
LA - eng
KW - orthomodular lattice; state; noncompatible pairs; (quasi)variety; orthomodular lattice; state; noncompatible pairs; (quasi)variety
UR - http://eudml.org/doc/30567
ER -

References

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