Ultra $LI$-Ideals in lattice implication algebras and $MTL$-algebras

Title:

Ultra $LI$-Ideals in lattice implication algebras and $MTL$-algebras

Creator:

Zhang, Xiaohong , Qin, Keyun , and Dudek, Wiesław Aleksander

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:3cde7e1b-09e8-4162-9b31-86c24f0d693f
uuid:3cde7e1b-09e8-4162-9b31-86c24f0d693f

Subject:

lattice implication algebra, $MTL$-algebra, (prime; ultra; obstinate; Boolean) $LI$-ideal, and $ILI$-ideal

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

591-605

Source:

Czechoslovak Mathematical Journal | 2007 Volume:57 | Number:2

Harvested from:

CDK

Metadata only:

false