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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

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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 
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     title = {Ultra $LI${-Ideals} in lattice implication algebras and $MTL$-algebras},
     journal = {Czechoslovak Mathematical Journal},
     pages = {591--605},
     year = {2007},
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     zbl = {1174.03349},
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     url = {http://geodesic.mathdoc.fr/item/CMJ_2007_57_2_a5/}
}
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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/

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