On Some Properties of Dedekind Lattices

Abstract

The objective of this paper is to study the Dedekind lattices, where we prove if is a -lattice and domain, then will be a Dedekind domain if and only if every non zero maximal element is invertible. On the other hand, we prove that if is a domain and -lattices, then is a dedehind domain if and only if is a UFD lattices and every non zero prime element is maximal.