Idempotent Elements in Multiplicative Lattices

In ١٩٦٢ R.P.Dilworth introduced the concept of a Noether lattice as an abstraction of the concept of the lattice of ideals of a Noetherian ring. He showed that many of the important theorems of classical ideal theory held in them. The purpose of this paper is to introduce and study the concept of idempotent elements for the multiplicative lattices , since they play very idempotent role for studying the multiplicative lattices and some rings.