On double basic algebras and pseudo-effect algebras
type: Item
instance of: scholarly article
title: On double basic algebras and pseudo-effect algebras
zbMATH Open document ID: 1235.06012
author: Ivan Chajda
author: Miroslav Kolařík
author: Jan Kühr
published in: Order
publication date: 2011-12-13T00:00:00Z
review text: Double basic algebras have been introduced in [\textit{I. Chajda}, ``Double basic algebras'', Order 26, No. 2, 149--162 (2009; Zbl 1173.06002)] as a counterpart of bounded lattices with order-antiautomorphisms on principal filters. Now their independent axiomatization is given. Double basic algebras represent a non-commutative extension of basic algebras which generalize orthomodular lattices in a similar way as MV-algebras generalize Boolean algebras. Lattice pseudo-effect algebras are characterized as a subvariety of double basic algebras and pairs of compatible elements of lattice pseudo-effect algebras are described in terms of double basic algebras.
reviewed by: Mirko Navara
Mathematics Subject Classification ID: 06D35
Mathematics Subject Classification ID: 03G12
Mathematics Subject Classification ID: 06C15
zbMATH DE Number: 5988081
zbMATH Keywords: basic algebra
zbMATH Keywords: double basic algebra
zbMATH Keywords: pseudo-MV-algebra
zbMATH Keywords: pseudo-effect algebra
zbMATH Keywords: compatibility
MaRDI profile type: Publication
full work available at URL: s11083-010-9187-8
OpenAlex ID: W2119054955
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DOI: 10.1007/S11083-010-9187-8
description: scientific article; zbMATH DE number 5988081