Pseudo EMV-algebras. I. basic properties

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F19%3A73597650" target="_blank" >RIV/61989592:15310/19:73597650 - isvavai.cz</a>

Result on the web

<a href="https://www.researchgate.net/publication/337464364_Pseudo_EMV-algebras_I_Basic_Properties" target="_blank" >https://www.researchgate.net/publication/337464364_Pseudo_EMV-algebras_I_Basic_Properties</a>

DOI - Digital Object Identifier

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Result language

angličtina

Original language name

Pseudo EMV-algebras. I. basic properties

Original language description

We introduce pseudo EMV-algebras which are a non-commutative generalization of both MV-algebras and generalized Boolean algebras. The existence of a top element is not assumed. The paper has two parts. In the present one we study basic properties of pseudo EMV-algebras as ideals and homomorphisms. The class of all pseudo EMV-algebras is not a variety and rather a more general class, called a q-variety, but similar to a variety. We study representable pseudo EMV-algebras, normal-valued ones, and pseudo EMV-algebras whose every maximal ideal is normal. The second part shows that every pseudo EMV-algebra without top element can be embedded into a pseudo EMV-algebra with top element as a maximal and normal ideal of the latter one. We present a categorical equivalence of the category of pseudo EMV-algebras without top element with a special category of pseudo MV-algebras or with a special category of ℓ-groups. Finally, we study states as finitely additive mappings as well as state-morphisms on pseudo EMV-algebras and we present their representation as an integral over a regular Borel probability measure.

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

2019

Confidentiality

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

Name of the periodical

Journal of Applied Logics-IfCoLoG Journal of Logics and their Applications

ISSN

2055-3706

e-ISSN

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Volume of the periodical

6

Issue of the periodical within the volume

7

Country of publishing house

GB - UNITED KINGDOM

Number of pages

43

Pages from-to

1285-1327

UT code for WoS article

000519571900005

EID of the result in the Scopus database

2-s2.0-85076982405