| Title:
|
Generalized prime $D$-filters of distributive lattices (English) |
| Author:
|
Phaneendra Kumar, A.P. |
| Author:
|
Sambasiva Rao, M. |
| Author:
|
Sobhan Babu, K. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
57 |
| Issue:
|
3 |
| Year:
|
2021 |
| Pages:
|
157-174 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The concept of generalized prime $D$-filters is introduced in distributive lattices. Generalized prime $D$-filters are characterized in terms of principal filters and ideals. The notion of generalized minimal prime $D$-filters is introduced in distributive lattices and properties of minimal prime $D$-filters are then studied with respect to congruences. Some topological properties of the space of all prime $D$-filters of a distributive lattice are also studied. (English) |
| Keyword:
|
dense element |
| Keyword:
|
filter |
| Keyword:
|
$D$-filter |
| Keyword:
|
prime $D$-filter |
| Keyword:
|
congruence |
| Keyword:
|
Hausdorff space |
| MSC:
|
06D99 |
| idZBL:
|
Zbl 07396181 |
| idMR:
|
MR4306175 |
| DOI:
|
10.5817/AM2021-3-157 |
| . |
| Date available:
|
2021-07-30T12:28:53Z |
| Last updated:
|
2021-11-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149019 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
|
[9] Phaneendra Kumar, A.P., Sambasiva Rao, M., Sobhan Babu, K.: Filters of distributive lattices generated by dense elements.to appear in Palestine J. Math. |
| Reference:
|
[10] Sambasiva Rao, M.: $e$-filters of MS-algebras.Acta Math. Sci. 33B (3) (2013), 738–746. MR 3048173, 10.1016/S0252-9602(13)60034-X |
| Reference:
|
[11] Sambasiva Rao, M., Badawy, A.: $\mu $-filters of distributive lattices.Southeast Asian Bull. Math. 40 (2016), 251–264. MR 3496685 |
| Reference:
|
[12] Speed, T.P.: Some remarks on a class of distributive lattices.J. Aust. Math. Soc. 9 (1969), 289–296. MR 0246800, 10.1017/S1446788700007205 |
| . |
