| Title:
|
$\alpha $-ideals and annihilator ideals in 0-distributive lattices (English) |
| Author:
|
Pawar, Y. S. |
| Author:
|
Khopade, S. S. |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
49 |
| Issue:
|
1 |
| Year:
|
2010 |
| Pages:
|
63-74 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In a 0-distributive lattice sufficient conditions for an $\alpha $-ideal to be an annihilator ideal and prime ideal to be an $\alpha $-ideal are given. Also it is proved that the images and the inverse images of $\alpha $-ideals are $\alpha $-ideals under annihilator preserving homomorphisms. (English) |
| Keyword:
|
0-distributive lattice |
| Keyword:
|
$\alpha $-ideal |
| Keyword:
|
annihilator ideal |
| Keyword:
|
quasi-complemented lattice |
| MSC:
|
06D99 |
| idZBL:
|
Zbl 1245.06023 |
| idMR:
|
MR2797524 |
| . |
| Date available:
|
2010-09-13T06:56:54Z |
| Last updated:
|
2013-09-18 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140738 |
| . |
| Reference:
|
[1] Balasubramani, P., Venkatanarsimhan: Characterizations of the 0-distributive lattice.Indian J. Pure Appl. Math. 32, 3 (2001), 315–324. MR 1826759 |
| Reference:
|
[2] Balasubramani, P.: Stone topology of the set of the set of prime filters of a 0-distributive lattice.Indian J. Pure Appl. Math. 35, 2 (2004), 149–158. MR 2040729 |
| Reference:
|
[3] Cornish, W. H.: Annulets and $\propto $-ideals in a distributive lattice.J. Aust. Math. Soc. 15, 1 (1975), 70–77. MR 0344170, 10.1017/S1446788700012775 |
| Reference:
|
[4] Grätzer, G.: Lattice Theory – First concepts and distributive lattices.Freeman and Company, San Francisco, 1971. MR 0321817 |
| Reference:
|
[5] Jayaram, C.: Prime $\alpha $-ideals in a 0-distributive lattice.Indian J. Pure Appl. Math. 17, 3 (1986), 331–337. Zbl 0595.06010, MR 0835346 |
| Reference:
|
[6] Pawar, Y. S., Mane, D. N.: $\alpha $-ideals in 0-distributive semilattices and 0-distributive lattices.Indian J. Pure Appl. Math. 24, 7-8 (1993), 435–443. Zbl 0789.06005, MR 1234802 |
| Reference:
|
[7] Varlet, J.: A generalization of the notion of pseudo-complementedness.Bull. Soc. Roy. Liege 37 (1968), 149–158. Zbl 0162.03501, MR 0228390 |
| . |
