O-Modularity and O-Distributivity in Semilattices

Abstract

In this paper we prove that every convex subordered set of an ordered set can be written as an intersection of a down-set and an up-set. We characterize o-modular and odistributive semilattices in terms of ideals of the semilattices. The notion of o-modular, odistributive and o-standard elements has been developed. We characterize the relation among the elements.