A ring R is left noetherian if and only if the direct sum of injective envelopes of any family of
left R-modules is the injective envelope of the direct sum of the given family of modules (or …

R wiil aiways denote a ring with identity element. All R-modules will be unital. Left
noetherian rings R are characterized by the fact that, for any family of injective left R …

We characterize locally Noetherian modules MR in terms of essential extensions of direct
sums of M-injective modules. As a special case (M= R) we obtain that the following …

THE EXISTENCE OF FLAT COVERS flat, then <j> is called a flat cover of M if F' F —^— MF (b)
¡ \ F —^ M Page 1 proceedings OF THE AMERICAN MATHEMATICAL SOCIETY Volume 122 …

It is known that every complex of left R-modules has an exact cover. We consider the
question of finding R for which every complex of left i?-modules has an exact envelope. We …

In § 1, we begin with a basic theorem which describes a convenient embedding of a
nonsingular left R-module into a complete direct product of copies of the left injective hull of …

1. Introduction. It is a well-known and basic result of homological alge-bra that the direct
product of an arbitrary family of injective modules over any ring is again injective [3, p. 8] …

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 …

Introduction* The concept of the" injective envelope" of a module was first given by Eckmann
and Schopf [2], although this terminology was first employed by Matlis [5]. The injective …

It is shown that any left module $ A $ over a ring $ R $ can be written as the intersection of a
downward directed system of injective submodules of an injective module; equivalently, as …