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

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

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

Original language description

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.

Czech name

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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

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OECD FORD branch

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

Project

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Continuities

S - Specificky vyzkum na vysokych skolach

Publication year

2021

Confidentiality

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

Name of the periodical

FUZZY SETS AND SYSTEMS

ISSN

0165-0114

e-ISSN

—

Volume of the periodical

418

Issue of the periodical within the volume

AUG-SI

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

25

Pages from-to

101-125

UT code for WoS article

000658282400006

EID of the result in the Scopus database

2-s2.0-85091689731