Geodesic
Ultra $LI$-Ideals in lattice implication algebras and $MTL$-algebras
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 2, pp. 591-605 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 03G10, 06B10, 54E15
Keywords: lattice implication algebra; $MTL$-algebra; (prime; ultra; obstinate; Boolean) $LI$-ideal; $ILI$-ideal 
@article{CMJ_2007_57_2_a5,
     author = {Zhang, Xiaohong and Qin, Keyun and Dudek, Wies{\l}aw A.},
     title = {Ultra $LI${-Ideals} in lattice implication algebras and $MTL$-algebras},
     journal = {Czechoslovak Mathematical Journal},
     pages = {591--605},
     year = {2007},
     volume = {57},
     number = {2},
     mrnumber = {2337617},
     zbl = {1174.03349},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2007_57_2_a5/}
}
TY  - JOUR
AU  - Zhang, Xiaohong
AU  - Qin, Keyun
AU  - Dudek, Wiesław A.
TI  - Ultra $LI$-Ideals in lattice implication algebras and $MTL$-algebras
JO  - Czechoslovak Mathematical Journal
PY  - 2007
SP  - 591
EP  - 605
VL  - 57
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/CMJ_2007_57_2_a5/
LA  - en
ID  - CMJ_2007_57_2_a5
ER  - 
%0 Journal Article
%A Zhang, Xiaohong
%A Qin, Keyun
%A Dudek, Wiesław A.
%T Ultra $LI$-Ideals in lattice implication algebras and $MTL$-algebras
%J Czechoslovak Mathematical Journal
%D 2007
%P 591-605
%V 57
%N 2
%U http://geodesic.mathdoc.fr/item/CMJ_2007_57_2_a5/
%G en
%F CMJ_2007_57_2_a5
Zhang, Xiaohong; Qin, Keyun; Dudek, Wiesław A. Ultra $LI$-Ideals in lattice implication algebras and $MTL$-algebras. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 2, pp. 591-605. http://geodesic.mathdoc.fr/item/CMJ_2007_57_2_a5/