In this work we introduce the concept of Zero element in an ADL analogous to that of least element in lattice and also we give different set of axioms which will characterize the class of ADL with zero. We will prove that these axioms are independent and also we give necessary and sufficient condition for an ADL with zero to be lattices and hence distributive lattices with least element.

Dissertation Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science in Mathematics