On a generalization of Heyting algebras I.

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F25%3A00637595" target="_blank" >RIV/67985840:_____/25:00637595 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s11225-024-10110-8" target="_blank" >https://doi.org/10.1007/s11225-024-10110-8</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11225-024-10110-8" target="_blank" >10.1007/s11225-024-10110-8</a>

Result language
angličtina
Original language name
On a generalization of Heyting algebras I.
Original language description
∇-algebra is a natural generalization of Heyting algebra, unifying many algebraic structures including bounded lattices, Heyting algebras, temporal Heyting algebras and the algebraic presentation of the dynamic topological systems. In a series of two papers, we will systematically study the algebro-topological properties of different varieties of ∇-algebras. In the present paper, we start with investigating the structure of these varieties by characterizing their subdirectly irreducible and simple elements. Then, we prove the closure of these varieties under the Dedekind-MacNeille completion and provide the canonical construction and the Kripke representation for ∇-algebras by which we establish the amalgamation property for some varieties of ∇-algebras. In the sequel of the present paper, we will complete the study by covering the logics of these varieties and their corresponding Priestley-Esakia and spectral duality theories.
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

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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