Ultra $LI$-Ideals in lattice implication algebras and $MTL$-algebras

Xiaohong Zhang; Ke Yun Qin; Wiesław Aleksander Dudek

Displaying similar documents to “Ultra $L I$ -Ideals in lattice implication algebras and $M T L$ -algebras”

Ultra $L I$ -ideals in lattice implication algebras

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

Czechoslovak Mathematical Journal

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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.

Annihilators in normal autometrized algebras

Ivan Chajda, Jiří Rachůnek (2001)

Czechoslovak Mathematical Journal

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The concepts of an annihilator and a relative annihilator in an autometrized $l$ -algebra are introduced. It is shown that every relative annihilator in a normal autometrized $l$ -algebra $𝒜$ is an ideal of $𝒜$ and every principal ideal of $𝒜$ is an annihilator of $𝒜$ . The set of all annihilators of $𝒜$ forms a complete lattice. The concept of an $I$ -polar is introduced for every ideal $I$ of $𝒜$ . The set of all $I$ -polars is a complete lattice which becomes a two-element chain provided $I$ is prime. The $I$ -polars...

$α$ -ideals and annihilator ideals in 0-distributive lattices

Y. S. Pawar, S. S. Khopade (2010)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In a 0-distributive lattice sufficient conditions for an $α$ -ideal to be an annihilator ideal and prime ideal to be an $α$ -ideal are given. Also it is proved that the images and the inverse images of $α$ -ideals are $α$ -ideals under annihilator preserving homomorphisms.

Displaying similar documents to “Ultra L I -Ideals in lattice implication algebras and M T L -algebras”