| Title:
|
Ultra $LI$-ideals in lattice implication algebras (English) |
| Author:
|
Qin, Keyun |
| Author:
|
Xu, Yang |
| Author:
|
Jun, Young Bae |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
52 |
| Issue:
|
3 |
| Year:
|
2002 |
| Pages:
|
463-468 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We define an ultra $LI$-ideal of a lattice implication algebra and give equivalent conditions for an $LI$-ideal to be ultra. We show that every subset of a lattice implication algebra which has the finite additive property can be extended to an ultra $LI$-ideal. (English) |
| Keyword:
|
lattice implication algebra |
| Keyword:
|
(ultra) $LI$-ideal |
| Keyword:
|
finite additive property |
| MSC:
|
03G10 |
| MSC:
|
06B10 |
| MSC:
|
54E15 |
| idZBL:
|
Zbl 1012.03061 |
| idMR:
|
MR1923253 |
| . |
| Date available:
|
2009-09-24T10:53:08Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127735 |
| . |
| Reference:
|
[1] Y. B. Jun, E. H. Roh and Y. Xu: $LI$-ideals in lattice implication algebras.Bull. Korean Math. Soc. 35 (1998), 13–24. MR 1609010 |
| Reference:
|
[2] Y. B. Jun and Y. Xu: Fuzzy $LI$-ideals in lattice implication algebras.J. Fuzzy Math. 7 (1999), 997–1003. MR 1734015 |
| Reference:
|
[3] Y. B. Jun, Y. Xu and K. Y. Qin: Positive implicative and associative filters of lattice implication algebras.Bull. Korean Math. Soc. 35(1) (1998), 53–61. MR 1608994 |
| Reference:
|
[4] Y. Xu: Homomorphisms in lattice implication algebras.Proc. of 5th Many-Valued Logical Congress of China (1992), 206–211. |
| Reference:
|
[5] Y. Xu: Lattice implication algebras.J. Southwest Jiaotong University 1 (1993), 20–27. Zbl 0966.03524 |
| Reference:
|
[6] Y. Xu and K. Y. Qin: On filters of lattice implication algebras.J. Fuzzy Math. 1 (1993), 251–260. MR 1230317 |
| . |
