Ultra LI-ideals in lattice implication algebras and MTL-algebras

被引：1
|
作者：
Xiaohong Zhang
Keyun Qin
Wiesław A. Dudek
机构：
[1] Ningbo University,Department of Mathematics, Faculty of Science
[2] Southwest Jiaotong University,Department of Applied Mathematics
[3] Wrocław University of Technology,Institute of Mathematics and Computer Science
来源：
Czechoslovak Mathematical Journal | 2007年 / 57卷
关键词：
lattice implication algebra; -algebra; (prime, ultra, obstinate, Boolean) ; -ideal; -ideal;
D O I：
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学科分类号：
摘要：
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.
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页码：591 / 605
页数：14
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