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Start Over Subject lattice implication algebra

1. Ultra $LI$-ideals in lattice implication algebras

Creator:
Qin, Keyun, Xu, Yang, and Jun, Young Bae
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
lattice implication algebra, (ultra) $LI$-ideal, and finite additive property
Language:
English
Description:
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.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

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

Creator:
Zhang, Xiaohong , Qin, Keyun , and Dudek, Wiesław Aleksander
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
lattice implication algebra, $MTL$-algebra, (prime; ultra; obstinate; Boolean) $LI$-ideal, and $ILI$-ideal
Language:
English
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.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public