It is proved that a module M over a commutative noetherian ring R is injective if Ext _ R^ i
((R/\mathfrak p) _\mathfrak p, M)= 0 Ext R i ((R/p) p, M)= 0 holds for every i\geqslant 1 i⩾ 1 …

Given a module E and a map M→ N of modules, all over a commutative ring R, it is shown
that if fHom (N, E)→ Hom (M, E) is injective then so is fHom (⋀ n N, E)→ Hom (⋀ n M, E) …

The object of this paper is to investigate finitely generated modules and injective modules
over fully bounded Noetherian rings. Our main results on fg modules (Theorems 3.1 and 3.4) …

We develop a technique to construct finitely injective modules which are non-trivial, in the
sense that they are not direct sums of injective modules. As a consequence, we prove that a …

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 and let $ S $ be an $ R $-algebra. It is well-known that if $ N
$ is an injective $ R $-module, then $\operatorname {Hom} _R (S, N) $ is an injective $ S …

Some theorems in [4] indicate that the injective modules over a ring R provide a great deal of
information about the structure of the ring. More recently, the papers of H. Bass [9] and C …

This note deals with a finitely generated faithful module E over a commutative semi-prime
noetherian ring R, with commutative endomorphism ring Hom R (E, E)= Ω (E). It is shown …

In this note we show that a countable injective module is $\sum $-injective and consequently
a ring $ R $ is left noetherian if the category of left $ R $-modules has a countable injective …

The notation in this paper will be standard and it may be found in [2] or [8]. Throughout the
paper, the notation A⊂'B will mean that A is an essential submodule of the module B. Given …