Minimal Prime Ideals in Almost Distributive Lattices
G. C. Rao, S. Ravi Kumar · 2009
If R is an ADL with 0, a minimal prime ideal belonging to an ideal I of R is defined. If I is an ideal of R, S is a multiplicatively closed subset of R such that I ∩F = ∅, then it is proved that there is a minimal prime ideal belonging to I such that M ∩ S = ∅. Finally it is proved that a prime ideal P of R is a minimal prime ideal of R if and only if for each x ∈ P, there is y/ ∈ P such that x ∧ y ∈ I.