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Currently displaying 1 – 2 of 2

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On ideals and congruences in BCC-algebras

Wiesław Aleksander Dudek; Xiaohong Zhang — 1998

Czechoslovak Mathematical Journal

We introduce a new concept of ideals in BCC-algebras and describe connections between such ideals and congruences.

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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