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

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

2007-10-20

arxiv.org/abs/0710.3887v1

Czechoslovak Math. J. vol. 57(132) (2007), 591--605

Mathematics

Logic

Scientific paper

A mistake concerning the ultra \textit{LI}-ideal of a lattice implication algebra is pointed out, and some new sufficient and necessary conditions for an \textit{LI}-ideal to be an ultra \textit{LI}-ideal are given. Moreover, the notion of an \textit{LI}-ideal is extended to MTL-algebras, the notions of a (prime, ultra, obstinate, Boolean) \textit{LI}-ideal and an \textit{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 \textit{LI}-ideal and Boolean \textit{LI}-ideal, (2) prime proper \textit{LI}-ideal and \textit{ILI}-ideal, (3) proper obstinate \textit{LI}-ideal, (4) ultra \textit{LI}-ideal.

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