Let R be a ring with identity. Given a positive integer n, a unitary right R-module X is called n–
injective provided, for every n-generated right ideal A of R, every R-homomorphism φ: A→ X …

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 …

For a ring A, it is proved that all A-modules are semiregular if and only if A is an Artinian
serial ring and J2(A)= 0. All rings are assumed to be associative and with nonzero identity …

Let ${P_R} $ be a projective module with trace ideal $ T $. An $ R $-module ${X_R} $ is $ T
$-accessible if $ XT= X.{\text {If}}{P_R} $ is finitely generated projective and $ C $ is the $ R …

In the second section we show that if J (M) is the radical of a module M over a near-ring R,
then J (M/J (M))= 0. Also, if A is a submodule of M and J (M/A)= 0, then J (M) g A. These …

In this note all rings are associative with identity elements and all modules are unital right
modules. Let I? be a ring and M a right R-module. Denote the socle and radical of M by Soc …

The problem of classifying properties of the endomorphism ring of a module in terms of
properties of the module is most naturally approached via a bijection between certain left or …

Let be a non-empty collection of right ideals of a ring R. A right R-module X is called-
injective provided each R-homomorphism ϕ: A→ X with A in can be lifted to an R …

Rings for which all modules have projective covers or for which all finitely generated
modules have projective covers have been studied extensively. These are the perfect and …

Recently KR Goodearl and D. Handelman [6] have studied simple regular rings from the
point of view of dimension-like functions. They have shown that there exists a unique …