Dual L-Almost Distributive Lattices
CJM Vol. 4 (December 2012), pp. 51 – 61.
Abstract:
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.
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