Galoitica: Journal of Mathematical Structures and Applications GJMSA 2834-5568 10.54216/GJSMA https://www.americaspg.com/journals/show/1474 2022 2022 Umm Al-Qura Univerity, Mekka, Saudi Arabia Khadija Ben Othman 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. 2023 2023 14 17 10.54216/GJMSA.030102 https://www.americaspg.com/articleinfo/33/show/1474