Representation and Embedding of PseudoMV-algebras with Square Roots II. Closures

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F24%3A73627588" target="_blank" >RIV/61989592:15310/24:73627588 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Representation and Embedding of PseudoMV-algebras with Square Roots II. Closures
Original language description
In [9], we started the investigation of pseudo MV-algebras with square roots. In the present paper, the main aim is to continue to study the structure of pseudo MV-algebras with square roots focusing on their new characterizations. The paper is divided into two parts. In the first part, we investigate the relationship between a pseudo MV-algebra with square root and its corresponding unital & ell;-group in the scene of two-divisibility. We characterize strict and non-strict square roots, and we describe square roots on strongly(H,1)-perfect pseudo MV-algebras. In the present second part, we find some conditions under which a particular class of pseudo MV-algebras can be embedded into pseudo MV-algebras with square roots. We compare both the concepts of a strict square root closure and a square root closure of a pseudo MV-algebra. We show that each MV-algebra has a square root closure. Finally, using the square root of individual elements of a pseudo MV-algebra, we find the greatest subalgebra of a special pseudo MV-algebra with weak square root.
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
10102 - Applied mathematics

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

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