Residuation in non-associative MV-algebras

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F18%3A73590107" target="_blank" >RIV/61989592:15310/18:73590107 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1515/ms-2017-0181" target="_blank" >http://dx.doi.org/10.1515/ms-2017-0181</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1515/ms-2017-0181" target="_blank" >10.1515/ms-2017-0181</a>

Result language

angličtina

Original language name

Residuation in non-associative MV-algebras

Original language description

It is well known that every MV-algebra can be converted into a residuated lattice satisfying divisibility and the double negation law. In a previous paper the first author and J. Kuhr introduced the concept of an NMV-algebra which is a non-associative modification of an MV-algebra. The natural question arises if an NMV-algebra can be converted into a residuated structure, too. Contrary to MV-algebras, NMV-algebras are not based on lattices but only on directed posets and the binary operation need not be associative and hence we cannot expect to obtain a residuated lattice but only an essentially weaker structure called a conditionally residuated poset. Considering several additional natural conditions we show that every NMV-algebra can be converted in such a structure. Also conversely, every such structure can be organized into an NMV-algebra. Further, we study an a bit more stronger version of an algebra where the binary operation is even monotone. We show that such an algebra can be organized into a residuated poset and, conversely, every residuated poset can be converted in this structure. (C) 2018 Mathematical Institute Slovak Academy of Sciences

Czech name

—

Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10101 - Pure mathematics

Project

—

Continuities

S - Specificky vyzkum na vysokych skolach

Publication year

2018

Confidentiality

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

Name of the periodical

Mathematica Slovaca

ISSN

0139-9918

e-ISSN

—

Volume of the periodical

68

Issue of the periodical within the volume

6

Country of publishing house

SK - SLOVAKIA

Number of pages

8

Pages from-to

1313-1320

UT code for WoS article

000451461500002

EID of the result in the Scopus database

2-s2.0-85057746665