An A-module M is catenary if for each pair of prime submodules K and L of M with $ K
{\subset} L $ all saturated chains of prime submodules of M from K to L have a common finite …

We generalise the concept of catenary rings to modules. We call an A-module M catenary if
for each pair of prime submodules K and L of M with K⊂ L all saturated chains of prime …

The purpose of the present paper is to prove some properties of the strongly irreducible
submodules in the arithmetical and Noetherian modules over a commutative ring. The …

Let M be a finitely generated torsion-free module over a generalized Dedekind domain D. It
is shown that if M is a projective D-module, then it is a generalized Dedekind module and v …

In this article the authors give the relation between a finitely-generated torsionfree Dedekind
module M over a domain R and prime submodules of the 𝒪 (M)-module M and the ring 𝒪 …

Let M be a finitely generated torsion-free module over a Dedekind domain R and M [X] be a
polynomial module over R [X], where X is an indeterminate. It is shown that M and M [X] are …

A right R-module M is (Goldie) finite dimensional (= fd) if M contains no infinite direct sums of
submodules. M is quotient fd (= qfd) if M/K is fd for all submodules K. A submodule I of M is …

Let R be a commutative ring with identity. A proper submodule N of an R-module M will be
called prime [resp. n-almost prime], if for r∈ R and a∈ M with ra∈ N [resp. ra∈ N\(N: M) n …

Matlis showed that an injective module over a commutative Noetherian ring R can be
completely decomposed as a direct sum of indecomposable injective submodules. In this …

Necessary and sufficient conditions are given for a module over a Dedekind domain to
satisfy the ascending chain condition on n-generated submodules for every positive integer …