DEDEKIND DOMAINS AND DEDEKIND MODULES
This work studies an interconnection between Dedekind domains and Dedekind modules. The interconnection will be investigated as an adoption of Noetherian and hereditary properties. Particularly, we show that a domain is a Dedekind domain if and only if its finitely generated torsion free uniform modules are Dedekind. The obtained result includes the case of noncommutative rings.
Dedekind domains, Dedekind modules, uniform modules.
