Disjunctive Ideals of Almost Distributive Lattices

• Published in: Discussiones mathematicae. General algebra and applications Vol. 42; no. 1; pp. 159 - 178
• Main Authors: Rafi, N., Srujana, M., Rao, T. Srinivasa
• Format: Journal Article
• Language: English
• 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

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...