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Prime O-ideals in almost distributive lattices. (English) Zbl 1349.06009

Summary: In this paper we derive some sufficient conditions for a prime ideal of an almost distributive lattice (ADL) to become an O-ideal. A set of equivalent conditions are established for every O-ideal to become an annihilator ideal. An equivalency is obtained between prime O-ideals and minimal prime ideals of an ADL. Finally, we obtain that any two distinct prime O-ideals of an ADL are co-maximal.

MSC:

06B10 Lattice ideals, congruence relations
06D75 Other generalizations of distributive lattices
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