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 …

Let $ R $ be a commutative ring with identity and $ D $ an $ R $-module. It is shown that if $
D $ is pure injective, then $ D $ is isomorphic to a direct summand of the direct product of a …

Let R be a commutative semilocal ring and U be the minimal injective cogenerator in the
category of R-modules. If R is almost noetherian, ie, each non-minimal prime ideal of R is …

163 NONZERO INJECTIVE COVERS OF MODULES Richard Belshoff and Jinzhong Xu
Abstract. We show that if R is a ring such that every n Page 1 VOLUME 13, NUMBER 3, FALL …

Suppose (R, m) and (S, n) are commutative Noetherian local rings and ϕ: R→ S is a flat
local homomorphism with the property that the induced homomorphism R/m→ S/mS is …

In this paper an example is given of a pair of commutative noetherian rings $ R\subseteq S $
with $ S $ a finite $ R $-module and $ IS\cap R= I $ for each ideal $ I $ of $ R $, but having …

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 …

INJECTTVE NEAR-RING MODULES OVER Z„ Page 1 PROCEEDINGS OF THE AMERICAN
MATHEMATICAL SOCIETY Volume 68, Number 1, January 1978 INJECTTVE NEAR-RING …

Let $ R $ be a commutative noetherian local ring. Denote by $\mod R $ the category of
finitely generated $ R $-modules, and by ${\mathcal G}(R) $ the full subcategory of $\mod R …

Throughout this paper we assume that all modules are finitely generated (left) modules over
a noetherian R-algebra A for a commutative local ring R. By a noetherian R-algebra A, we …