Disjunctive Ideals of Almost Distributive Lattices

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. A necessary and sufficient condition is derived for an inverse homomorphic image of a disjunctive ideal of an ADL to be aga...

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Published inDiscussiones mathematicae. General algebra and applications Vol. 42; no. 1; pp. 159 - 178
Main Authors Rafi, N., Srujana, M., Rao, T. Srinivasa
Format Journal Article
LanguageEnglish
Published Sciendo 01.03.2022
University of Zielona Góra
Subjects
06D15
06D99
Almost Distributive Lattice (ADL)
disjunctive ideal
minimal prime ideal
normal ADL
normal prime ideal
strongly disjunctive ideal
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Abstract 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. A necessary and sufficient condition is derived for an inverse homomorphic image of a disjunctive ideal of an ADL to be again a disjunctive ideal. Later, the concept of strongly disjunctive ideals is introduced in an ADL and their properties are studied. Some equivalent conditions are established for the set of all strongly disjunctive ideals to convert into a sublattice of the ideal lattice.
AbstractList Abstract only
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. A necessary and sufficient condition is derived for an inverse homomorphic image of a disjunctive ideal of an ADL to be again a disjunctive ideal. Later, the concept of strongly disjunctive ideals is introduced in an ADL and their properties are studied. Some equivalent conditions are established for the set of all strongly disjunctive ideals to convert into a sublattice of the ideal lattice.
Author Rafi, N.
Rao, T. Srinivasa
Srujana, M.
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  givenname: T. Srinivasa
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  email: tsnivas@gmail.com
  organization: Department of Mathematics, Bapatla Engineering College, Bapatla, Andhra Pradesh, India-522 101
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SubjectTerms 06D15
06D99
Almost Distributive Lattice (ADL)
disjunctive ideal
minimal prime ideal
normal ADL
normal prime ideal
strongly disjunctive ideal
Title Disjunctive Ideals of Almost Distributive Lattices
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