MV-algebras and their corresponding Bézout domains

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F24%3A73627586" target="_blank" >RIV/61989592:15310/24:73627586 - isvavai.cz</a>
Result on the web
<a href="https://www.tandfonline.com/doi/epdf/10.1080/00927872.2024.2367165" target="_blank" >https://www.tandfonline.com/doi/epdf/10.1080/00927872.2024.2367165</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1080/00927872.2024.2367165" target="_blank" >10.1080/00927872.2024.2367165</a>

Result language
angličtina
Original language name
MV-algebras and their corresponding Bézout domains
Original language description
The paper studies the interplay between MV-algebras, Bezout domains, and Abelian l-groups, which was initiated by Y. C. Yang in 2006. For each MV-algebra M=Gamma(G,u) , we delve into some properties of a subset of a Bezout domain corresponding to M. We study Boolean elements and ideals within the MV-algebra, focusing on their correspondence to subsets of Bezout domains. This investigation aids us in classifying Bezout domains about directly indecomposable MV-algebras or subdirect products of MV-algebras. We establish that each MV-algebra associated with a Noetherian Bezout domain is finite. In conclusion, from a ring-theoretical perspective, we present characteristics of perfect MV-algebras, (H,1)-perfect MV-algebras, hyperarchimedean MV-algebras, and complete MV-algebras.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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