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 in | Discussiones mathematicae. General algebra and applications Vol. 42; no. 1; pp. 159 - 178 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Sciendo
01.03.2022
University of Zielona Góra |
Subjects | |
Online Access | Get full text |
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Summary: | 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. |
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ISSN: | 1509-9415 2084-0373 |
DOI: | 10.7151/dmgaa.1384 |