A variety containing EMV-algebras and Pierce sheaves of EMV-algebras

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F21%3A73609916" target="_blank" >RIV/61989592:15310/21:73609916 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0165011420303626" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0165011420303626</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.fss.2020.09.011" target="_blank" >10.1016/j.fss.2020.09.011</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A variety containing EMV-algebras and Pierce sheaves of EMV-algebras

Popis výsledku v původním jazyce

According to [11], we know that the class of all EMV-algebras, EMV, is not a variety, since it is not closed under the subalgebra operator. The main aim of this work is to find the least variety containing EMV. For this reason, we introduced the variety wEMV of wEMV-algebras of type (2, 2, 2, 2, 0) induced by some identities. We show that, adding a derived binary operation circle minus to each EMV-algebra (M; boolean OR, boolean AND, circle plus, 0), we extend its language, so that (M; boolean OR, &amp;AND, circle plus, circle minus, 0), called an associated wEMV-algebra, belongs to wEMV. Then using the congruence relations induced by the prime ideals of a wEMV-algebra, we prove that each wEMV-algebra can be embedded into an associated wEMV-algebra. We show that wEMV is the least subvariety of the variety of wEMV-algebras containing EMV. Finally, we study Pierce sheaves of proper EMV-algebras.

Název v anglickém jazyce

A variety containing EMV-algebras and Pierce sheaves of EMV-algebras

Popis výsledku anglicky

According to [11], we know that the class of all EMV-algebras, EMV, is not a variety, since it is not closed under the subalgebra operator. The main aim of this work is to find the least variety containing EMV. For this reason, we introduced the variety wEMV of wEMV-algebras of type (2, 2, 2, 2, 0) induced by some identities. We show that, adding a derived binary operation circle minus to each EMV-algebra (M; boolean OR, boolean AND, circle plus, 0), we extend its language, so that (M; boolean OR, &amp;AND, circle plus, circle minus, 0), called an associated wEMV-algebra, belongs to wEMV. Then using the congruence relations induced by the prime ideals of a wEMV-algebra, we prove that each wEMV-algebra can be embedded into an associated wEMV-algebra. We show that wEMV is the least subvariety of the variety of wEMV-algebras containing EMV. Finally, we study Pierce sheaves of proper EMV-algebras.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2021

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

—

Svazek periodika

418

Číslo periodika v rámci svazku

AUG-SI

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

25

Strana od-do

101-125

Kód UT WoS článku

000658282400006

EID výsledku v databázi Scopus

2-s2.0-85091689731