Properties and Special Filters of Pseudocomplemented Posets

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F25%3A73633209" target="_blank" >RIV/61989592:15310/25:73633209 - isvavai.cz</a>
Result on the web
<a href="https://arxiv.org/pdf/2312.04685v1" target="_blank" >https://arxiv.org/pdf/2312.04685v1</a>
DOI - Digital Object Identifier
—

Result language
angličtina
Original language name
Properties and Special Filters of Pseudocomplemented Posets
Original language description
Investigating the structure of pseudocomplemented lattices started and this structure was essentially developed by G. Gratzer. In recent years, some special filters in pseudocomplemented and Stone lattices have been studied by M. Sambasiva Rao. However, in some applications, in particular in non-classical logics with unsharp logical connectives, pseudocomplemented posets instead of lattices are used. This motivated us to develop an algebraic theory of pseudocomplemented posets, i.e. we derive identities and inequalities holding in such posets and we use them in order to characterize the so-called Stone posets. Then we adopt several concepts of special filters and we investigate their properties in pseudocomplemented posets. Moreover, we show how properties of these filters influence algebraic properties of the underlying pseudocomplemented posets.
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

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

Similar results(10)