A theorem of Cartan-Eilenberg (Cartan, H., Eilenberg, S.(1956). Homological Algebra.
Princeton: Princeton University Press, pp. 390.) states that a ring R is right Noetherian iff …

Let R be a ring. An R-module X is called c-injective if, for every closed submodule L of every
R-module M, every homomorphism from L to X lifts to M. It is proved that if R is a Dedekind …

Let R be a commutative ring with unit, T an R-module, and na positive integer. It is proved
that T is n-flat over R if B⊗ RT is B-torsionfree for each n–generated commutative R-algebra …

Let R be a ring. A right R-module M is said to be neat-flat if the kernel of any epimorphism
Y→ M is neat in Y, ie, the induced map Hom (S, Y)→ Hom (S, M) is surjective for any simple …

The concept of a module M being almost N-injective, where N is some module, was
introduced by Baba (1989). For a given module M, the class of modules N, for which M is …

Let ${P_R} $ be a projective module with trace ideal $ T $. An $ R $-module ${X_R} $ is $ T
$-accessible if $ XT= X.{\text {If}}{P_R} $ is finitely generated projective and $ C $ is the $ R …

In a recent paper, Aydoǧdu and López-Permouth have defined a module M to be N-
subinjective if every homomorphism N→ M extends to some E (N)→ M, where E (N) is the …

We say that over an arbitrary ring a module M has the property (CWE)(respectively,(CWEE))
if M has a weak supplement (respectively, ample weak supplements) in every cofinite …

Given a flat local ring homomorphism R → SR→ S and two finitely generated R-modules M
and N, we describe conditions under which the modules\rm Tor^ R _ i (M, N) Tor i R (M, N) …

JVe mean by a local ring a (not necessarily Noetherian) ring with 1 which contains only one
maximal left ideal. Our concern is with commutative local rings over which finitely generated …