Residuation in twist products and pseudo-Kleene posets

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F22%3A73609455" target="_blank" >RIV/61989592:15310/22:73609455 - isvavai.cz</a>

Výsledek na webu

<a href="https://mb.math.cas.cz/full/147/3/mb147_3_7.pdf" target="_blank" >https://mb.math.cas.cz/full/147/3/mb147_3_7.pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.21136/MB.2021.0182-20" target="_blank" >10.21136/MB.2021.0182-20</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Residuation in twist products and pseudo-Kleene posets

Popis výsledku v původním jazyce

M. Busaniche, R. Cignoli (2014), C. Tsinakis and A. M. Wille (2006) showed that every residuated lattice induces a residuation on its full twist product. For their construction they used also lattice operations. We generalize this problem to left-residuated groupoids which need not be lattice-ordered. Hence, we cannot use the same construction for the full twist product. We present another appropriate construction which, however, does not preserve commutativity and associativity of multiplication. Hence we introduce the so-called operator residuated posets to obtain another construction which preserves the mentioned properties, but the results of operators on the full twist product need not be elements, but may be subsets. We apply this construction also to restricted twist products and present necessary and sufficient conditions under which we obtain a pseudo-Kleene operator residuated poset.

Název v anglickém jazyce

Residuation in twist products and pseudo-Kleene posets

Popis výsledku anglicky

M. Busaniche, R. Cignoli (2014), C. Tsinakis and A. M. Wille (2006) showed that every residuated lattice induces a residuation on its full twist product. For their construction they used also lattice operations. We generalize this problem to left-residuated groupoids which need not be lattice-ordered. Hence, we cannot use the same construction for the full twist product. We present another appropriate construction which, however, does not preserve commutativity and associativity of multiplication. Hence we introduce the so-called operator residuated posets to obtain another construction which preserves the mentioned properties, but the results of operators on the full twist product need not be elements, but may be subsets. We apply this construction also to restricted twist products and present necessary and sufficient conditions under which we obtain a pseudo-Kleene operator residuated poset.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GF20-09869L" target="_blank" >GF20-09869L: Ortomodularita z různých pohledů</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

Mathematica Bohemica

ISSN

0862-7959

e-ISSN

2464-7136

Svazek periodika

147

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

15

Strana od-do

369-383

Kód UT WoS článku

000712909500001

EID výsledku v databázi Scopus

2-s2.0-85139953921