On Some Properties of Dedekind Lattices

Khadija Ben Othman

Umm Al-Qura Univerity, Mekka, Saudi Arabia

Emails: khagijabenothman33@gmail.com

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.

Keywords: Lattice; UFD; Principal Ideal; Domain; PG-Lattice