| Title:
|
Ultra $LI$-Ideals in lattice implication algebras and $MTL$-algebras (English) |
| Author:
|
Zhang, Xiaohong |
| Author:
|
Qin, Keyun |
| Author:
|
Dudek, Wiesław A. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
57 |
| Issue:
|
2 |
| Year:
|
2007 |
| Pages:
|
591-605 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A mistake concerning the ultra $LI$-ideal of a lattice implication algebra is pointed out, and some new sufficient and necessary conditions for an $LI$-ideal to be an ultra $LI$-ideal are given. Moreover, the notion of an $LI$-ideal is extended to $MTL$-algebras, the notions of a (prime, ultra, obstinate, Boolean) $LI$-ideal and an $ILI$-ideal of an $MTL$-algebra are introduced, some important examples are given, and the following notions are proved to be equivalent in $MTL$-algebra: (1) prime proper $LI$-ideal and Boolean $LI$-ideal, (2) prime proper $LI$-ideal and $ILI$-ideal, (3) proper obstinate $LI$-ideal, (4) ultra $LI$-ideal. (English) |
| Keyword:
|
lattice implication algebra |
| Keyword:
|
$MTL$-algebra |
| Keyword:
|
(prime |
| Keyword:
|
ultra |
| Keyword:
|
obstinate |
| Keyword:
|
Boolean) $LI$-ideal |
| Keyword:
|
$ILI$-ideal |
| MSC:
|
03G10 |
| MSC:
|
06B10 |
| MSC:
|
54E15 |
| idZBL:
|
Zbl 1174.03349 |
| idMR:
|
MR2337617 |
| . |
| Date available:
|
2009-09-24T11:47:53Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128192 |
| . |
| Reference:
|
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| Reference:
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