The concepts of ideals and filters is introduced in lattices where filters are the dual of ideals. This class of ideals and filters in lattices includes proper, prime, maximal, and normal ideals and filters. Prime ideals and filters are characterized in terms of maximal ideals and filters and vice versa depending the types of lattices. The concept of semi-prime ideals and filters is discussed in a general lattice by generalizing the notion of O-distributive lattices and several characterizations of semi-prime ideals and filters are included. Here we give different properties of minimal prime ideals and filters containing a semi-prime ideal and filter in proving some interesting results. In addition, the concept of normal ideals and filters, and normlets are introduced in distributive lattice. Normal ideals and filters characterized in terms of normlets. Disjunctive lattices are characterized in terms of normal ideals and filters. Finally, we discussed properties of prime normal ideals and filters and give conclusion.

A Dissertation submitted to Bahir Dar University in partial fulfillment of the requirements for the Degree Master of Science in Mathematics.