Central elements of effect algebras
type: Item
instance of: scholarly article
title: Central elements of effect algebras
zbMATH Open document ID: 1075.81012
author: Josef Tkadlec
published in: International Journal of Theoretical Physics
publication date: 2005-03-15T00:00:00Z
review text: An element \(a\) of an effect algebra \((E,0,1,\oplus)\) is called principal, if \(b\leq a, c\leq a\) implies \(b\oplus c\leq a\). An element \(a\) of \(E\) is called central, if (1) \(a\) and its orthosupplement \(a'\) are principal, and (2) \(b=(b\wedge a)\oplus(b\wedge a')\) for any \(b\in L\). The author shows that condition (2) on \(a\) may be weakened to (2'): \(b\wedge a = b\wedge a'=0\) implies \(b=0\), and the sets \([0,a]\cap[0,b], [0,a']\cap[0,b]\) have maximal elements for any \(b\in E\). This generalizes the authors result from [Tatra Mt. Math. Publ. 10, 55--62 (1997; Zbl 0915.06003)].
reviewed by: Horst Szambien
Mathematics Subject Classification ID: 81P10
Mathematics Subject Classification ID: 06C15
Mathematics Subject Classification ID: 03G12
zbMATH DE Number: 2146148
zbMATH Keywords: effect algebra
zbMATH Keywords: central element
zbMATH Keywords: weak distributivity
zbMATH Keywords: orthoalgebra
zbMATH Keywords: quantum logic
MaRDI profile type: Publication
full work available at URL: b:ijtp.0000048621.17418.bb
OpenAlex ID: W2052540625
DOI: 10.1023/B:IJTP.0000048621.17418.BB
description: scientific article; zbMATH DE number 2146148