| Title:
|
$\alpha $-ideals in De Morgan residuated lattices (English) |
| Author:
|
Wu, Supeng |
| Author:
|
An, Xiaogang |
| Author:
|
Liu, Hui |
| Author:
|
Yang, Jiang |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
62 |
| Issue:
|
4 |
| Year:
|
2026 |
| Pages:
|
675-701 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The main purpose of this paper is to study the lattice structure of $\alpha$-ideals and investigate the hull-kernel topology on prime $\alpha$-ideals in a De Morgan residuated lattice. First, the lattice structure of all $\alpha$-ideals in a De Morgan residuated lattice is studied and it is proved that the set of all $\alpha$-ideals forms a complete Heyting algebra. Furthermore, by means of annihilator operators, the concept of quasi-complemented De Morgan residuated lattices is proposed and some equivalent conditions are derived for them. Finally, the space of all prime $\alpha$-ideals is studied and it is stated that the space is a spectral space. In addition, some conditions are given for the space to be a Hausdorff space. Some topological characterizations of quasi-complemented De Morgan residuated lattices are demonstrated. (English) |
| Keyword:
|
De Morgan residuated lattice |
| Keyword:
|
$\alpha $-ideal |
| Keyword:
|
prime $\alpha $-ideal |
| Keyword:
|
quasi-complemented De Morgan residuated lattice |
| Keyword:
|
hull-kernel topology |
| MSC:
|
03G10 |
| MSC:
|
03G25 |
| MSC:
|
06D35 |
| MSC:
|
06F05 |
| DOI:
|
10.14736/kyb-2026-4-0675 |
| . |
| Date available:
|
2026-10-07T10:22:26Z |
| Last updated:
|
2026-10-07 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153779 |
| . |
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| . |
