Commutativity in orthomodular posets
type: Item
instance of: scholarly article
title: Commutativity in orthomodular posets
zbMATH Open document ID: 0549.06002
DOI: 10.1016/0034-4877(80)90095-6
author: R. M. Godowski
published in: Reports on Mathematical Physics
publication date: 1980-01-01T00:00:00Z
review text: Although he finds motivation for his paper in the axiomatic approach to quantum mechanics, of Mackie and Maczynski, the author is here presenting an abstract mathematical discussion of the commutation relation in orthomodular posets. The author gives a very clear and concise summary of previous results, especially as they concern regular, and also Boolean orthomodular posets. He generalises a result due to Guz, showing that if an orthomodular poset P is Boolean, then aCb iff \(a\wedge b\) exists in P. He also presents a method of constructing Boolean orthomodular posets which are not regular - i.e. which have mutually compatible elements which are not contained in a single Boolean subalgebra. Although there is no discussion of physical considerations here, such results are clearly of special interest to those concerned with the axiomatic, or orthomodular, approach to quantum mechanics.
Mathematics Subject Classification ID: 06A06
Mathematics Subject Classification ID: 06C15
Mathematics Subject Classification ID: 81P10
zbMATH DE Number: 3875346
zbMATH Keywords: orthomodular posets
zbMATH Keywords: Boolean orthomodular posets
zbMATH Keywords: compatible elements
zbMATH Keywords: quantum mechanics
MaRDI profile type: Publication
full work available at URL: 0034-4877(80)90095-6
OpenAlex ID: W2008863299
cites work: On the structure of quantum logic
cites work: Q5723020
cites work: Boolean properties of observables in axiomatic quantum mechanics
cites work: Q5682356
cites work: Q5537293
description: scientific article; zbMATH DE number 3875346