In relation to degenerations of modules, we introduce several partial orders on the set of
isomorphism classes of finitely generated modules over a noetherian commutative local …

We prove that neat and coneat submodules of a module coincide when is a commutative
ring such that every maximal ideal is principal, extending a recent result by Fuchs. We …

In this note, we ask when the class of all finitely generated reflexive (torsionless) left
modules is closed under extensions. This is not always the case, even if R is left and right …

Abstract Let (R, 𝔪) (R,\frakm) be a commutative Noetherian local ring. In this paper, it is
shown that the going-up theorem holds for R⊆ R ̂ R⊆R if and only if Rad (I+ Ann RA)= 𝔪 …

Let R be a commutative ring, and let L and L′ be R-modules. We investigate finiteness
conditions (eg, noetherian, artinian, mini-max, Matlis reflexive) of the modules Ext R i (L, L′) …

A well-known result of Köthe and Cohen-Kaplansky states that a commutative ring R has the
property that every R-module is a direct sum of cyclic modules if and only if R is an Artinian …

Let R be a commutative noetherian ring. Denote by mod\, R mod R the category of finitely
generated R-modules. In this paper, we study n-torsionfree modules in the sense of …

Let A be a commutative ring and let E be an A-module with a finite free resolution (see below
for definition). Extending results known previously for noetherian rings, it is shown that ${\text …

For any module M over a commutative ring R with identity, we consider Sch (M) as a certain
class of prime submodules modulo the equivalence relation that two such prime …

Motivated by work of CU Jensen, R.-O. Buchweitz, and H. Flenner, we prove the following
result. Let $ R $ be a commutative noetherian ring and $\mathfrak {a} $ an ideal in the …