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Ultra L I -ideals in lattice implication algebras

Ke Yun Qin, Yang Xu, Young Bae Jun (2002)

Czechoslovak Mathematical Journal

We define an ultra L I -ideal of a lattice implication algebra and give equivalent conditions for an L I -ideal to be ultra. We show that every subset of a lattice implication algebra which has the finite additive property can be extended to an ultra L I -ideal.

Ultra L I -Ideals in lattice implication algebras and M T L -algebras

Xiaohong Zhang, Ke Yun Qin, Wiesław Aleksander Dudek (2007)

Czechoslovak Mathematical Journal

A mistake concerning the ultra L I -ideal of a lattice implication algebra is pointed out, and some new sufficient and necessary conditions for an L I -ideal to be an ultra L I -ideal are given. Moreover, the notion of an L I -ideal is extended to M T L -algebras, the notions of a (prime, ultra, obstinate, Boolean) L I -ideal and an I L I -ideal of an M T L -algebra are introduced, some important examples are given, and the following notions are proved to be equivalent in M T L -algebra: (1) prime proper L I -ideal and Boolean L I -ideal,...

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