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) …

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 …

ABSTRACT A submodule N of a module M is δ-small in M if N+ X≠ M for any proper
submodule X of M with M∕ X singular. A projective δ-cover of a module M is a projective …

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 …

Sandomierski (Proc. AMS 21 (1969), 205–207) has proved that a ring is semiperfect if and
only if every simple module has a projective cover. This is generalized to semiperfect …

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 …

Cofinitely δM−Supplemented and Cofinitely δM−Semiperfect Modules 1 Introduction Page 1
International Journal of Algebra, Vol. 5, 2011, no. 32, 1575 - 1588 Cofinitely δM−Supplemented …

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 …

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 …