Archimedean Classes in Integral Commutative Residuated Chains

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F09%3A00159057" target="_blank" >RIV/68407700:21230/09:00159057 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

Archimedean Classes in Integral Commutative Residuated Chains

Original language 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 (qp) 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

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

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Continuities

Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2009

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Mathematical Logic Quarterly

ISSN

0942-5616

e-ISSN

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Volume of the periodical

55

Issue of the periodical within the volume

3

Country of publishing house

DE - GERMANY

Number of pages

17

Pages from-to

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UT code for WoS article

000267096600010

EID of the result in the Scopus database

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