Ultra <Emphasis Type="Italic">LI</Emphasis>-ideals in lattice implication algebras and <Emphasis Type="Italic">MTL</Emphasis>-algebras |
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| Authors: | Xiaohong Zhang Keyun Qin Wiesław A Dudek |
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| Institution: | (1) Department of Mathematics, Faculty of Science, Ningbo University, Ningbo, 315211 Zhejiang Province, P. R. China;(2) Department of Applied Mathematics, Southwest Jiaotong University, Chengdu, Sichuan, 610031, P. R. China;(3) Institute of Mathematics and Computer Science, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland |
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| Abstract: | 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.
This work was supported by the Zhejiang Provincial Natural Science Foundation of China (Grant No. Y605389) and K. C. Wong
Magna Fund in Ningbo University. |
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| Keywords: | lattice implication algebra MTL-algebra (prime ultra obstinate Boolean) LI-ideal ILI-ideal |
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