Displaying similar documents to “On annihilators in BL-algebras”

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

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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...

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.

δ -ideals in pseudo-complemented distributive lattices

M. Sambasiva Rao (2012)

Archivum Mathematicum

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The concept of δ -ideals is introduced in a pseudo-complemented distributive lattice and some properties of these ideals are studied. Stone lattices are characterized in terms of δ -ideals. A set of equivalent conditions is obtained to characterize a Boolean algebra in terms of δ -ideals. Finally, some properties of δ -ideals are studied with respect to homomorphisms and filter congruences.