… for any ring R a module E is an indecomposable, injective module if … -Noetherian ring, then
every injective Jϋ-module has a decomposition as a direct sum of indecomposable, injective …

… theory for injective modules over a commutative Noetherian ring. … -module, we shall use
E(M) to denote the injective envelope … injective modules over a commutative Noetherian ring. …

… or of a weaker condition than injectivity. In Section 2, we prove that R is a w-Noetherian
ring if and only if the direct limit of the GV -torsion-free injective modules is injective. The main …

… has an injective resolution. To see that such resolutions exist we first take an injective module
E … Then, for any A-module A, the obvious map A-->EHomA(A ,) is a monomorphism into an …

… injective modules over commutative Noetherian rings. It led us to examine the interaction
between the injective modules … in the context of noncommutative Noetherian rings. Let 8 be a …

… Noetherian ring then pf = p^y Matlis [6] has used localization to show that injective modules
over a commutative Noetherian ring are … a right Noetherian ring. Also see Theorems 7 and 8. …

… Hence Rp is a Noetherian ring. It is easily seen that the canonical map E -+ Ep is an
isomorphism of R-modules, and we may consider E as an injective R,-module. Furthermore, …

… product of injective modules over a commutative ring again injective2'? When the ring is an
… In case of noetherian rings, we will give a condition for an affirmativ& answer and its several …

… injective modules. For instance, M. Okado [10] proved that, over a right noetherian ring, an
extending module … We also show that a module over a right noetherian ring is extending if and …

… ring A for R, every injective A-module possesses a … is an injective module over the commutative
Noetherian ring A and … with an injective module E over the commutative Noetherian ring A…