c-ideals in complemented posets
| Autor: | Ivan Chajda, Miroslav Kolařík, Helmut Länger |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | Mathematica Bohemica, Vol 149, Iss 3, Pp 305-316 (2024) |
| Druh dokumentu: | article |
| ISSN: | 0862-7959 2464-7136 |
| DOI: | 10.21136/MB.2023.0108-22 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
| Externí odkaz: |
|