A representation of weak effect algebras
type: Item
instance of: scholarly article
title: A representation of weak effect algebras
zbMATH Open document ID: 1274.03098
published in: Mathematica Slovaca
publication date: 2012-08-27T00:00:00Z
Mathematics Subject Classification ID: 03G12
Mathematics Subject Classification ID: 06D35
Mathematics Subject Classification ID: 06F20
zbMATH DE Number: 6072856
zbMATH Keywords: weak effect algebra
zbMATH Keywords: weak basic algebra
zbMATH Keywords: directoid
zbMATH Keywords: antitone involution
author: Ivan Chajda
MaRDI profile type: Publication
full work available at URL: s12175-012-0034-9
OpenAlex ID: W2062390512
cites work: Every effect algebra can be made into a total algebra
DOI: 10.2478/S12175-012-0034-9
review text: Effect algebras [\textit{ {D.~J. Foulis}} and \textit{ {M.~K. Bennett}}, Found. Phys. 24, No. 10, 1331--1352 (1994; Zbl 1213.06004)] are partial algebras which play a significant role in the theory of partially ordered abelian groups. To overcome the problems that a partial operation implies for the applicability of universal-algebraic methods, the author, \textit{ {R. Halaš}} and \textit{ {J. Kühr}} have introduced in [Algebra Univers. 61, No. 2, 139--150 (2009; Zbl 1192.03048)] a way to extend the partial addition to a total one, being led to so-called weak basic algebras. Concerning the converse direction, however, a weak basic algebra does not in general give rise to an effect algebra. The present paper focusses for this reason on weak effect algebras, which generalise effect algebras and should not be mixed with the partial algebras studied by the reviewer in [\textit{ {T. Vetterlein}}, J. Electr. Eng. 54, No. 12/s, 61--64 (2003; Zbl 1062.03065)] under the same name. A mutual correspondence between weak effect algebras and weak basic algebras is established.
reviewed by: Thomas Vetterlein
description: scientific article; zbMATH DE number 6072856