| Title:
|
Indexed annihilators in lattices (English) |
| Author:
|
Chajda, Ivan |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
31 |
| Issue:
|
4 |
| Year:
|
1995 |
| Pages:
|
259-262 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The concept of annihilator in lattice was introduced by M. Mandelker. Although annihilators have some properties common with ideals, the set of all annihilators in $L$ need not be a lattice. We give the concept of indexed annihilator which generalizes it and we show the basic properties of the lattice of indexed annihilators. Moreover, distributive and modular lattices can be characterized by using of indexed annihilators. (English) |
| Keyword:
|
lattice |
| Keyword:
|
distributive lattice |
| Keyword:
|
modular lattice |
| Keyword:
|
annihilator |
| Keyword:
|
ideal |
| Keyword:
|
indexed annihilator |
| MSC:
|
06B10 |
| MSC:
|
06C05 |
| MSC:
|
06D05 |
| MSC:
|
06D15 |
| idZBL:
|
Zbl 0860.06005 |
| idMR:
|
MR1390584 |
| . |
| Date available:
|
2008-06-06T21:29:16Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107546 |
| . |
| Reference:
|
[1] Davey, B., Nieminen, J.: Annihilators in modular lattices.Algebra Univ. 22 (1986), 154-158. MR 0870463 |
| Reference:
|
[2] Mandelker, M.: Relative annihilators in lattices.Duke Math. J. 40 (1970), 377-386. Zbl 0206.29701, MR 0256951 |
| . |
