1. bookVolume 42 (2022): Issue 1 (March 2022)
Journal Details
License
Format
Journal
eISSN
2084-0373
First Published
16 Apr 2017
Publication timeframe
2 times per year
Languages
English
access type Open Access

Disjunctive Ideals of Almost Distributive Lattices

Published Online: 05 Apr 2022
Volume & Issue: Volume 42 (2022) - Issue 1 (March 2022)
Page range: 159 - 178
Received: 26 Apr 2020
Accepted: 23 Dec 2020
Journal Details
License
Format
Journal
eISSN
2084-0373
First Published
16 Apr 2017
Publication timeframe
2 times per year
Languages
English
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.

Keywords

MSC 2010

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