The concept of injective modules, introduced by B. Eckmann-A. Schopf in 1953, is among
the most fundamental tools in module and ring theory (cf. for example [7]). In [11], a …

Let R be a ring with Jacobson radical J. Bass [1] called R semi-perfect if the factor ring R/J is
semi-simple Artinian and every idempotent of R/J can be lifted to an idempotent of R. He …

A submodule A of a left module B (over an associative ring with 1) is pure if for any right
module F, the natural homomorphism F⊗ A→ F⊗ B is injective. A module C is pure-injective …

Ring Ouasi-Frobenius? Page 1 oURNAL OF ALGEBRA 165, 531–542 (1994) When Is a Self-Injective
Semiperfect Ring Ouasi-Frobenius? JOHN CLARK Department of Mathematics and Statistics …

Let RP be a projective R-module which is not finitely generated. Let E= End R (P). This
paper examines the structure of P as an E-module and relations between right ideals of R …

Let R be a commutative ring, M be an R-module, and w be the so-called w-operation on R.
Set S w={f∈ R [X]| c (f) w= R}, where c (f) denotes the content of f. Let R {X}= R [X] S w and M …

Introduction. A ring is called left (right) hereditary in case each left (right) ideal is projective.
Such rings have been studied extensively, and the property of being left hereditary is …

The study of direct sums and direct products of R-modules is usually related to the question
of transfer of a property" P" on R-modules: When do direct sums or direct products of R …

H-rings and Co-H-rings have been defined by K. Oshiro in [9]. A ring R is a right H-ring (Co-
H-ring) iff every injective (projective) right R-module is lifting (extending). A right H-ring or a …

Alt the rings we consider will be associative with 1~ 0; all the ring homomorphisms will be
required to preserve the identity elements. All the modules we consider will be unitary …