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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.

Median prime ideals of pseudo-complemented distributive lattices

M. Sambasiva Rao — 2022

Archivum Mathematicum

Coherent ideals, strongly coherent ideals, and τ -closed ideals are introduced in pseudo-complemented distributive lattices and their characterization theorems are derived. A set of equivalent conditions is derived for every ideal of a pseudo-complemented distributive lattice to become a coherent ideal. The notion of median prime ideals is introduced and some equivalent conditions are derived for every maximal ideal of a pseudo-complemented distributive lattice to become a median prime ideal which...

Coaxial filters of distributive lattices

M. Sambasiva Rao — 2023

Archivum Mathematicum

Coaxial filters and strongly coaxial filters are introduced in distributive lattices and some characterization theorems of p m -lattices are given in terms of co-annihilators. Some properties of coaxial filters of distributive lattices are studied. The concept of normal prime filters is introduced and certain properties of coaxial filters are investigated. Some equivalent conditions are derived for the class of all strongly coaxial filters to become a sublattice of the filter lattice.

Filters of lattices with respect to a congruence

M. Sambasiva RaoAbd El-Mohsen Badawy — 2014

Discussiones Mathematicae - General Algebra and Applications

Some properties of filters on a lattice L are studied with respect to a congruence on L. The notion of a θ-filter of L is introduced and these filters are then characterized in terms of classes of θ. For distributive L, an isomorphism between the lattice of θ-filters of L and the lattice of filters of L / θ is obtained.

Generalized prime D -filters of distributive lattices

A.P. Phaneendra KumarM. Sambasiva RaoK. Sobhan Babu — 2021

Archivum Mathematicum

The concept of generalized prime D -filters is introduced in distributive lattices. Generalized prime D -filters are characterized in terms of principal filters and ideals. The notion of generalized minimal prime D -filters is introduced in distributive lattices and properties of minimal prime D -filters are then studied with respect to congruences. Some topological properties of the space of all prime D -filters of a distributive lattice are also studied.

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