Dual L-Almost Distributive Lattices

In this paper, the concept of a dual $L$−Almost Distributive Lattice (Dual $L$−ADL) is introduced as a generalization of a dual $L$−algebra. Different necessary and sufficient conditions for an ADL to become a dual $L$−ADL are derived. It is proved that every dual $L$−ADL is a dual Stone Almost Distributive Lattice as well as a dually Normal Almost Distributive Lattice. A dual $L$−ADL is characterized in terms of its principal ideals and prime ideals.