Varieties of orthomodular lattices related to states
type: Item
instance of: scholarly article
title: Varieties of orthomodular lattices related to states
zbMATH Open document ID: 0581.06006
DOI: 10.1007/BF01195144
author: René Mayet
published in: Algebra Universalis
publication date: 1985-01-01T00:00:00Z
review text: This is a very good paper which should be recommended to anyone interested in orthomodular structures. The main question asked and analyzed there is as follows: Given a preassigned property P of the state space, when the class of all orthomodular lattices whose state spaces satisfy P forms a variety? Apart from the obvious algebraic interest, this question is also relevant to the axiomatics of quantum theories. Using Birkhoff's characterization of varieties, the author develops a method for pursuing the above question. The results which he obtains may in the reviewer's view iniciate a new branch of lattice theory. (As a by- product the paper solves an open question posed by \textit{R. Godowski} [Demonstr. Math. 15, 817-822 (1982; Zbl 0522.06010)].)
Mathematics Subject Classification ID: 06C15
Mathematics Subject Classification ID: 06B20
Mathematics Subject Classification ID: 81P10
zbMATH DE Number: 3929072
zbMATH Keywords: orthomodular lattices
zbMATH Keywords: state spaces
zbMATH Keywords: axiomatics of quantum theories
zbMATH Keywords: characterization of varieties
reviewed by: Pavel Pták
MaRDI profile type: Publication
cites work: Q3952094
cites work: Varieties of Orthomodular Lattices
cites work: Varieties of Orthomodular Lattices. II
cites work: Astroids and pastings
cites work: VARIETIES OF ORTHOMODULAR LATTICES WITH A STRONGLY FULL SET OF STATES
cites work: STATES ON ORTHOMODULAR LATTICES
cites work: SOME EQUATIONS RELATED TO STATES ON ORTHOMODULAR LATTICES
cites work: Orthomodular lattices admitting no states
cites work: Q4750696
cites work: Q3891824
cites work: Q4100556
cites work: Jauch–Piron states
cites work: Q5847989
full work available at URL: https://doi.org/10.1007/bf01195144
OpenAlex ID: W1973862080
description: scientific article; zbMATH DE number 3929072