C-ideals in complemented posets

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F24%3A73621057" target="_blank" >RIV/61989592:15310/24:73621057 - isvavai.cz</a>
Result on the web
<a href="https://mbpapers.math.cas.cz/full/149/3/mb149_3_3.pdf" target="_blank" >https://mbpapers.math.cas.cz/full/149/3/mb149_3_3.pdf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.21136/MB.2023.0108-22" target="_blank" >10.21136/MB.2023.0108-22</a>

Result language
angličtina
Original language name
C-ideals in complemented posets
Original language description
In their recent paper on posets with a pseudocomplementation denoted by * the first and the third author introduced the concept of a *-ideal. This concept is in fact an extension of a similar concept introduced in distributive pseudocomplemented lattices and semilattices by several authors, see References. Now we apply this concept of a c-ideal (dually, c-filter) to complemented posets where the complementation need neither be antitone nor an involution, but still satisfies some weak conditions. We show when an ideal or filter in such a poset is a c-ideal or c-filter, and we prove basic properties of them. Finally, we prove the so-called separation theorems for c-ideals. The text is illustrated by several examples.
Czech name
—
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
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GF20-09869L" target="_blank" >GF20-09869L: The many facets of orthomodularity</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

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

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