Ultra LI-ideals in lattice implication algebras and MTL-algebras
Logic
2015-01-27 v1 General Mathematics
Abstract
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.
Keywords
Cite
@article{arxiv.0710.3887,
title = {Ultra LI-ideals in lattice implication algebras and MTL-algebras},
author = {Xiaohong Zhang and Keyun Qin and Wieslaw A. Dudek},
journal= {arXiv preprint arXiv:0710.3887},
year = {2015}
}