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 …

Let R be a ring with Jacobson radical J (R). Following CNI, a submodule N of a left R-
module RM is said to lie over a summand of M if there exists an idempotent e E End (RM) …

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 R be a ring with Jacobson radical J. A projective left R-module P was called by Mares [3]
a semi-perfect module if every homomorphic image of P has a projective cover, while P is …

Semi-perfect and perfect modules were introduced by Mares [3] as generalizations of
Bass'[2] notions of semi-perfect and perfect rings. She developed a substantial structure …

The notion of generalized projective covers Is Introduced to give a natural generalization of
a theorem of Bass on perfect rings. Moreover, In terms of this notion, some characterizations …

For a ring R and a right R-module M, a submodule N of M is said to be δ-small in M if,
whenever N+ X= M with M/X singular, we have X= M. If there exists an epimorphism p: P→ M …

In this paper we shall generalize the notion of semiperfect modules in terms of preradicals,
and show that almost all properties of semiperfect modules are preserved under this …

In this work, we prove that an R-module M is cofinitely δ-supplemented (ie each cofinite
submodule of M has a δ-supplement) if and only if every maximal submodule of M has a δ …

It is well known that a projective module M is⊕-supplemented if and only if M is semiperfect.
We show that a projective module M is⊕-cofinitely supplemented if and only if M is cofinitely …