A representation of symmetric Wajsberg pseudo hoops

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F25%3A73633943" target="_blank" >RIV/61989592:15310/25:73633943 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0165011425002805" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0165011425002805</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.fss.2025.109541" target="_blank" >10.1016/j.fss.2025.109541</a>

Result language
angličtina
Original language name
A representation of symmetric Wajsberg pseudo hoops
Original language description
This paper explores Wajsberg pseudo hoops derived from filters of bounded Wajsberg pseudo hoops, also known as pseudo MV-algebras. Extending the known result from [1] that every Wajsberg hoop is a maximal filter of an MV-algebra, we introduce symmetric Wajsberg pseudo hoops as a variety encompassing Wajsberg hoops. We demonstrate that every normal filter of a bounded Wajsberg pseudo hoop is an ultrafilter of an appropriate bounded Wajsberg pseudo hoop. Introducing a new binary operation circle star on Wajsberg pseudo hoops, we focus on symmetric Wajsberg pseudo hoops. We establish that each such hoop H is isomorphic to the pseudo hoop induced by a filter of a Wajsberg pseudo hoop A(H), with A(H) unique up to isomorphism. By analyzing the relationship between normal prime (maximal) filters of H and A(H), we establish a necessary and sufficient condition for their representability, deepening the understanding of the structural properties of these algebraic systems.
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
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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