Generalization of short modules

الملخص EN

It is proved that, if R is a commutative local Noetherian ring, then an R-module M is (almost) short and coatomic if and only if it is Noetherian.

Also, for a Dedekind Domain R and R-module M, M is (almost) short if and only if M is Noetherian or M contains a Noetherian submodule N such that M N is (almost) short and is the injective hull of a simple R-module.