Coatomic modules over Dedekind domains

Abstract

Let R be a ring with identity and M a unital right R-module. In this note some properties of coatomic modules are studied and it is shown that the following are equivalent for a module M over a Dedekind domain R: (1) M is a coatomic module. (2) Every submodule of M is coatomic. (3) M/L is reduced for every submodule L of M.