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Exploring Star Filters of Almost Distributive Lattices

Axioms
In an almost distributive lattice (ADL), we have presented and explored the notions of star filters and starlets. Further, we have characterized star filters through their starlets.
Ali Al Khabyah, Noorbhasha Rafi, Moin A. Ansari   +2 more
doaj   +5 more sources

Disjunctive Ideals of Almost Distributive Lattices

Discussiones Mathematicae - General Algebra and Applications, 2022
The concept of disjunctive ideals is introduced in an Almost Distributive Lattice (ADL). It is proved that the set of all disjunctive ideals of an ADL forms a complete lattice.
Rafi N., Srujana M., Rao T. Srinivasa
doaj   +3 more sources

On Quasi-P-Almost Distributive Lattices

Discussiones Mathematicae - General Algebra and Applications, 2020
In this paper, the concept of quasi pseudo-complementation on an Almost Distributive Lattice (ADL) as a generalization of pseudo-complementation on an ADL is introduced and its properties are studied.
Bandaru Ravi Kumar, Rao G.C.
doaj   +4 more sources

Weak Relative Complements in Almost Distributive Lattices

Discussiones Mathematicae - General Algebra and Applications, 2018
In this paper, the concept of relative complementation in almost distributive lattice is generalized. We obtain several properties on the sets of weak relative complement elements.
Sirisetti Ramesh, Jogarao G.
doaj   +3 more sources

β-Prime Spectrum of Stone Almost Distributive Lattices

Discussiones Mathematicae - General Algebra and Applications, 2020
The notion of boosters and β-filters in stone Almost Distributive Lattices are introduced and their properties are studied, utilizing boosters to characterize the β-filters.
Rafi N., Bandaru Ravi Kumar
doaj   +3 more sources

Weakly 2-Absorbing Ideals in Almost Distributive Lattices

Journal of Mathematics, 2022
The concepts of weakly 2-absorbing ideal and weakly 1-absorbing prime ideal in an almost distributive lattice (ADL) are introduced, and the necessary conditions for a weakly 1-absorbing prime ideal to become a weakly 2-absorbing ideal in algebraic form ...
Natnael Teshale Amare
doaj   +3 more sources

On coaxial filters of almost distributive lattices

Discussiones Mathematicae - General Algebra and Applications
Summary: In an Almost Distributive Lattice (ADL), coaxial filters and strongly coaxial filters are presented, and various characterization theorems of dually normal ADLs are given in terms of dual annihilators. Several characteristics of ADL coaxial filters are investigated.
Noorbhasha Rafi, Mukkamala Sambasiva Rao
doaj   +4 more sources

Finite distributive lattices are congruence lattices of almost-geometric lattices [PDF]

Algebra Universalis, 2011
It is proven that any finite distributive lattice is isomorphic to the lattice of congruences of some finite semimodular lattice having the additional property that the poset of nonzero join-irreducible elements is the cardinal sum of chains having at most two elements.
Gabor Czedli, Czedli Gabor
exaly   +3 more sources

On α-Multiplier on Almost Distributive Lattices

Journal of Mathematics, 2021
In this paper, we initiate the concept of α-multiplier on almost distributive lattices. We prove some useful results by using the notion of α-multiplier and generalize the idea of multiplier on almost distributive lattices.
Ying Wang, Abid Mahboob, Abdul Rauf Khan, Zafar Ullah, Zahid Karim, Mamoona Karim   +5 more
doaj   +2 more sources

w−FILTERS OF ALMOST DISTRIBUTIVE LATTICES [PDF]

Journal of Algebraic Systems
The notion of w−filters is introduced in an Almost Distributive Lattice(ADL) and properties are investigated. A necessary and sufficient condition is derived for a maximal filter of an ADL to become a w−filter which leads to a characterization of a quasi-
Noorbasha Rafi, Vijay Pavuluri, Balaiah Mothukuri   +2 more
doaj   +3 more sources