Congruences and ideals in pseudo effect algebras as total algebras
type: Item
instance of: scholarly article
title: Congruences and ideals in pseudo effect algebras as total algebras
zbMATH Open document ID: 1209.03052
author: Sylvia Pulmannová
author: Elena Vinceková
published in: Soft Computing
publication date: 2010-08-23T00:00:00Z
review text: Congruences and ideals in pseudo-effect algebras and their total algebra versions are studied. It is shown that every congruence of the total algebra induces a Riesz congruence in the corresponding pseudo-effect algebra. Conversely, to every normal Riesz ideal in a pseudo-effect algebra there is a total algebra in which the given ideal induces a congruence of the total algebra. Ideals of total algebras corresponding to lattice-ordered pseudo-effect algebras are characterized and it is shown that they coincide with normal Riesz ideals in the pseudo-effect algebras.
reviewed by: Josef Tkadlec
Mathematics Subject Classification ID: 03G12
Mathematics Subject Classification ID: 06C15
Mathematics Subject Classification ID: 81P10
zbMATH DE Number: 5774077
zbMATH Keywords: pseudo-effect algebra
zbMATH Keywords: ideal
zbMATH Keywords: congruence
zbMATH Keywords: commutative directoid
MaRDI profile type: Publication
full work available at URL: s00500-009-0532-z
OpenAlex ID: W2017806721
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DOI: 10.1007/S00500-009-0532-Z
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description: scientific article; zbMATH DE number 5774077