We characterize a ring over which every left module of finite length has an injective hull of
finite length. Using this, we show that finite normalizing extensions of such a ring also have …

ON THE RINGS WHOSE INJECTIVE HULLS ARE FLAT 1. Introduction Let R be a
commutative Noetherian ring with nonzero identity and let Page 1 PROCEEDINGS OF THE …

1. Introduction. The concept of continuous modules owes its origin to Von Neumann's work
on continuous geometries [16], and Utumi's work on continuous rings ([12],[13],[14]). L …

Let R be a ring, and let S be the injective hull of the right regular module RR. Suppose that S
can be made into a ring with multiplication compatible with that of R. Osofsky, in 1964, asked …

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 …

In the previous paper [4] the author and T. Ishii studied the endomorphism rings of
noetherian quasi-injective modules. As an application of it, we consider, in this paper, quasi …

Let R be a ring, and for an R-module, let E (M) denote the injective envelope of M. Following
Sharpe and Vamos ([2], Sec. 4.4) we say R is an H-ring if for distinct simple R-modules S1 …

Introduction In this discussion every module over a ring R will be understood to be a left i2-
module. R will always have a unit, and every module will be unitary. The aim of this paper is …

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. Let $ T={\oplus _ {i\in I}} E (R/{M_i}) $ and $ W=\prod\nolimits _ {i\in I}{E
(R/{M_i})} $, where each ${M_i} $ is a maximal right ideal and $ E (A) $ is the injective hull of …