Monadic GMV-algebras
type: Item
instance of: scholarly article
title: Monadic GMV-algebras
zbMATH Open document ID: 1151.06007
author: Jiří Rachůnek
author: Dana Šalounová
published in: Archive for Mathematical Logic
publication date: 2008-08-18T00:00:00Z
full work available at URL: http://hdl.handle.net/10084/65996
review text: In a recent paper, there appeared plenty new algebraic models that were inspired by Łukasiewicz many-valued calculus. They generalized MV-algebras not assuming commutativity any more. One such algebraic model are the GMV-algebras, introduced by the first author and independently by \textit{G. Georgescu} and \textit{A. Iorgulescu} [``Pseudo-MV algebras'', Mult.-Valued Log. 6, No. 1--2, 95--135 (2001; Zbl 1014.06008)]. These algebras are always an interval in a unital \(\ell\)-group with strong unit. The authors introduce monadic GMV-algebras and study also polyadic GMV-algebra. Some relations among ideals and congruences, and among varieties are shown.
reviewed by: Anatolij Dvurečenskij
Mathematics Subject Classification ID: 06D35
Mathematics Subject Classification ID: 03B50
Mathematics Subject Classification ID: 06F05
Mathematics Subject Classification ID: 06F15
zbMATH DE Number: 5313051
zbMATH Keywords: monadic GMV-algebra
zbMATH Keywords: quantifier
zbMATH Keywords: left adjoint mapping
zbMATH Keywords: polyadic GMV-algebra
zbMATH Keywords: ideals
zbMATH Keywords: congruences
zbMATH Keywords: varieties
MaRDI profile type: Publication
OpenAlex ID: W2013877382
Wikidata QID: Q59288500
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DOI: 10.1007/S00153-008-0086-2
description: scientific article; zbMATH DE number 5313051