| Title:
|
Coaxial filters of distributive lattices (English) |
| Author:
|
Sambasiva Rao, M. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
59 |
| Issue:
|
5 |
| Year:
|
2023 |
| Pages:
|
397-409 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Coaxial filters and strongly coaxial filters are introduced in distributive lattices and some characterization theorems of $pm$-lattices are given in terms of co-annihilators. Some properties of coaxial filters of distributive lattices are studied. The concept of normal prime filters is introduced and certain properties of coaxial filters are investigated. Some equivalent conditions are derived for the class of all strongly coaxial filters to become a sublattice of the filter lattice. (English) |
| Keyword:
|
filter |
| Keyword:
|
co-annihilator |
| Keyword:
|
coaxial filter |
| Keyword:
|
strongly coaxial filter |
| Keyword:
|
$pm$-lattice |
| Keyword:
|
normal prime filter |
| MSC:
|
06D99 |
| idZBL:
|
Zbl 07790555 |
| idMR:
|
MR4641954 |
| DOI:
|
10.5817/AM2023-5-397 |
| . |
| Date available:
|
2023-08-15T13:37:49Z |
| Last updated:
|
2024-02-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151796 |
| . |
| Reference:
|
[1] Birkhoff, G.: Lattice theory.Third edition American Mathematical Society Colloquium Publications, vol. XXV, American Mathematical Society, Providence, R.I., 1967. Zbl 0153.02501, MR 0227053 |
| Reference:
|
[2] Burris, S., Sankappanavar, H.P.: A Course in Universal Algebra.Springer Verlag, 1981. Zbl 0478.08001, MR 0648287 |
| Reference:
|
[3] Cornish, W.H.: Normal lattices.J. Aust. Math. Soc. 14 (1972), 200–215. MR 0313148, 10.1017/S1446788700010041 |
| Reference:
|
[4] Cornish, W.H.: Annulets and $\alpha $-ideals in distributive lattices.J. Aust. Math. Soc. 15 (1973), 70–77. MR 0344170, 10.1017/S1446788700012775 |
| Reference:
|
[5] Mandelker, M.: Relative annihilators in lattices.Duke Math. J. 37 (1970), 377–386. Zbl 0206.29701, MR 0256951, 10.1215/S0012-7094-70-03748-8 |
| Reference:
|
[6] Pawar, Y.S., Thakare, N.K.: $pm$-lattice.Algebra Universalis 7 (1977), 259–263. MR 0434910, 10.1007/BF02485435 |
| Reference:
|
[7] Rao, M. Sambasiva: Normal filters of distributive lattices.Bull. Sect. Logic Univ. Łódź 41 (3) (2012), 131–143. MR 3066566 |
| Reference:
|
[8] Rao, M. Sambasiva: $\mu $-filters of distributive lattices.Southeast Asian Bull. Math. 40 (2016), 251–264. MR 3496685 |
| Reference:
|
[9] Speed, T.P.: Some remarks on a class of distributive lattices.J. Aust. Math. Soc. 9 (1969), 289–296. MR 0246800, 10.1017/S1446788700007205 |
| . |
