A representation of symmetric Wajsberg pseudo hoops

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F25%3A73633943" target="_blank" >RIV/61989592:15310/25:73633943 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0165011425002805" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0165011425002805</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.fss.2025.109541" target="_blank" >10.1016/j.fss.2025.109541</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A representation of symmetric Wajsberg pseudo hoops

Popis výsledku v původním jazyce

This paper explores Wajsberg pseudo hoops derived from filters of bounded Wajsberg pseudo hoops, also known as pseudo MV-algebras. Extending the known result from [1] that every Wajsberg hoop is a maximal filter of an MV-algebra, we introduce symmetric Wajsberg pseudo hoops as a variety encompassing Wajsberg hoops. We demonstrate that every normal filter of a bounded Wajsberg pseudo hoop is an ultrafilter of an appropriate bounded Wajsberg pseudo hoop. Introducing a new binary operation circle star on Wajsberg pseudo hoops, we focus on symmetric Wajsberg pseudo hoops. We establish that each such hoop H is isomorphic to the pseudo hoop induced by a filter of a Wajsberg pseudo hoop A(H), with A(H) unique up to isomorphism. By analyzing the relationship between normal prime (maximal) filters of H and A(H), we establish a necessary and sufficient condition for their representability, deepening the understanding of the structural properties of these algebraic systems.

Název v anglickém jazyce

A representation of symmetric Wajsberg pseudo hoops

Popis výsledku anglicky

This paper explores Wajsberg pseudo hoops derived from filters of bounded Wajsberg pseudo hoops, also known as pseudo MV-algebras. Extending the known result from [1] that every Wajsberg hoop is a maximal filter of an MV-algebra, we introduce symmetric Wajsberg pseudo hoops as a variety encompassing Wajsberg hoops. We demonstrate that every normal filter of a bounded Wajsberg pseudo hoop is an ultrafilter of an appropriate bounded Wajsberg pseudo hoop. Introducing a new binary operation circle star on Wajsberg pseudo hoops, we focus on symmetric Wajsberg pseudo hoops. We establish that each such hoop H is isomorphic to the pseudo hoop induced by a filter of a Wajsberg pseudo hoop A(H), with A(H) unique up to isomorphism. By analyzing the relationship between normal prime (maximal) filters of H and A(H), we establish a necessary and sufficient condition for their representability, deepening the understanding of the structural properties of these algebraic systems.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název periodika

FUZZY SETS AND SYSTEMS

ISSN

0165-0114

e-ISSN

1872-6801

Svazek periodika

519

Číslo periodika v rámci svazku

NOV

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

14

Strana od-do

"109541-1"-"109541-14"

Kód UT WoS článku

001540937700001

EID výsledku v databázi Scopus

2-s2.0-105011264272