Residuation in non-associative MV-algebras

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Residuation in non-associative MV-algebras

Popis výsledku v původním jazyce

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

Název v anglickém jazyce

Residuation in non-associative MV-algebras

Popis výsledku anglicky

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

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název periodika

Mathematica Slovaca

ISSN

0139-9918

e-ISSN

—

Svazek periodika

68

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

SK - Slovenská republika

Počet stran výsledku

8

Strana od-do

1313-1320

Kód UT WoS článku

000451461500002

EID výsledku v databázi Scopus

2-s2.0-85057746665