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$𝒵$ -distributive function lattices

Marcel Erné (2013)

Mathematica Bohemica

It is known that for a nonempty topological space $X$ and a nonsingleton complete lattice $Y$ endowed with the Scott topology, the partially ordered set $[X, Y]$ of all continuous functions from $X$ into $Y$ is a continuous lattice if and only if both $Y$ and the open set lattice $𝒪 X$ are continuous lattices. This result extends to certain classes of $𝒵$ -distributive lattices, where $𝒵$ is a subset system replacing the system $𝒟$ of all directed subsets (for which the $𝒟$ -distributive complete lattices are just the continuous...

$*$ -median

Bohumil Šmarda (1996)

Mathematica Slovaca

$ℱ$ -multipliers and the localization of MV-algebras.

Buşneag, Dumitru, Piciu, Dana (2003)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

0-distributive posets

Khalid A. Mokbel, Vilas S. Kharat (2013)

Mathematica Bohemica

Several characterizations of 0-distributive posets are obtained by using the prime ideals as well as the semiprime ideals. It is also proved that if every proper $l$ -filter of a poset is contained in a proper semiprime filter, then it is $0$ -distributive. Further, the concept of a semiatom in 0-distributive posets is introduced and characterized in terms of dual atoms and also in terms of maximal annihilator. Moreover, semiatomic 0-distributive posets are defined and characterized. It is shown that...

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

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

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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

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.