Geodesic
Orthomodular lattices with state-separated noncompatible pairs
Czechoslovak Mathematical Journal, Tome 50 (2000) no. 2, pp. 359-366.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 
@article{CMJ_2000__50_2_a10,
     author = {Mayet, R. and Pt\'ak, P.},
     title = {Orthomodular lattices with state-separated noncompatible pairs},
     journal = {Czechoslovak Mathematical Journal},
     pages = {359--366},
     publisher = {mathdoc},
     volume = {50},
     number = {2},
     year = {2000},
     mrnumber = {1761393},
     zbl = {1047.06005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2000__50_2_a10/}
}
TY  - JOUR
AU  - Mayet, R.
AU  - Pták, P.
TI  - Orthomodular lattices with state-separated noncompatible pairs
JO  - Czechoslovak Mathematical Journal
PY  - 2000
SP  - 359
EP  - 366
VL  - 50
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMJ_2000__50_2_a10/
LA  - en
ID  - CMJ_2000__50_2_a10
ER  - 
%0 Journal Article
%A Mayet, R.
%A Pták, P.
%T Orthomodular lattices with state-separated noncompatible pairs
%J Czechoslovak Mathematical Journal
%D 2000
%P 359-366
%V 50
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMJ_2000__50_2_a10/
%G en
%F CMJ_2000__50_2_a10
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/