DISTRIBUTIVE SUBSEMILATTICE

摘要

Generalization of distributive ideal to convex subsemilattice is called distributive convex subsemilattice or distributive subsemilattice. This paper deals with the above concept and the three characterization theorems (Theorems 3.1, 3.2 and 3.5) for distributive subsemilattice. The relation of distributive subsemilattice with the distributive ideal, standard ideal and neutral ideal is also established. Further its relation with the congruence class is also established. It is proved that the intersection of two distributive subsemilattices is either a distributive subsemilattice or it is empty.