Ultra LI-ideals in lattice implication algebras and MTL-algebras
Xiaohong Zhang, Keyun Qin, Wiesław A. Dudek · Czechoslovak Mathematical Journal · 2007
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.