About: Archimedean Classes in Integral Commutative Residuated Chains

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	This paper investigates a quasi-variety of representable integral commutative residuated lattices axiomatized by the quasi-identity resulting from the well-known Wajsberg identity (p q) q (q p) p if it is written as a quasi-identity, i. e., (p q) q 1 (q p) p 1. We prove that this quasi-identity is strictly weaker than the corresponding identity. On the other hand, we show that the resulting quasi-variety is in fact a variety and provide an axiomatization. The obtained results shed some light on the structure of Archimedean integral commutative residuated chains. Further, they can be applied to various subvarieties of MTL-algebras, for instance we answer negatively Hájek's question asking whether the variety of MTL-algebras is generated by its Archimedean members This paper investigates a quasi-variety of representable integral commutative residuated lattices axiomatized by the quasi-identity resulting from the well-known Wajsberg identity (p q) q (q p) p if it is written as a quasi-identity, i. e., (p q) q 1 (q p) p 1. We prove that this quasi-identity is strictly weaker than the corresponding identity. On the other hand, we show that the resulting quasi-variety is in fact a variety and provide an axiomatization. The obtained results shed some light on the structure of Archimedean integral commutative residuated chains. Further, they can be applied to various subvarieties of MTL-algebras, for instance we answer negatively Hájek's question asking whether the variety of MTL-algebras is generated by its Archimedean members (en)
Title	Archimedean Classes in Integral Commutative Residuated Chains Archimedean Classes in Integral Commutative Residuated Chains (en)
skos:prefLabel	Archimedean Classes in Integral Commutative Residuated Chains Archimedean Classes in Integral Commutative Residuated Chains (en)
skos:notation	RIV/68407700:21230/09:00159057!RIV10-MSM-21230___
http://linked.open...avai/riv/aktivita	Z
http://linked.open...avai/riv/aktivity	Z(MSM6840770038)
http://linked.open...iv/cisloPeriodika	3
http://linked.open...vai/riv/dodaniDat	2010
http://linked.open...aciTvurceVysledku	Horčík, Rostislav
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	České vysoké učení technické v Praze / Fakulta elektrotechnická
http://linked.open...dnocenehoVysledku	303987
http://linked.open...ai/riv/idVysledku	RIV/68407700:21230/09:00159057
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	NORM BASED LOGIC; FUZZY LOGICS; LATTICES; ALGEBRAS; PROOF (en)
http://linked.open.../riv/klicoveSlovo	ALGEBRAS LATTICES FUZZY LOGICS NORM BASED LOGIC PROOF
http://linked.open...odStatuVydavatele	DE - Spolková republika Německo
http://linked.open...ontrolniKodProRIV	[DBB1BE487D26]
http://linked.open...i/riv/nazevZdroje	Mathematical Logic Quarterly
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...UplatneniVysledku	2009
http://linked.open...v/svazekPeriodika	55
http://linked.open...iv/tvurceVysledku	Horčík, Rostislav
http://linked.open...ain/vavai/riv/wos	000267096600010
http://linked.open...n/vavai/riv/zamer	Decision Making and Control for Manufacturing III
issn	0942-5616
number of pages	17 (xsd:int)
http://localhost/t...ganizacniJednotka	21230

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