Transitive and Absorbent Filters of Implicative Almost Distributive Lattices - Berhanu Assaye Alaba; Mihret Alamneh; Tilahun Mekonnen (LPPM Institut Teknologi Sepuluh Nopember, 2018)
In this paper, we introduce the concept of transitive and absorbent filters of implicative almost distributive lattices and studied their properties. A necessary and sufficient condition is derived for every filter to become a transitive filter. Some sufficient conditions are also derived for a filter to become a transitive filter. A set of equivalent conditions is obtained for a filter to become an absorbent filter.