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 …

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 and M a right R-module. M is called⊕-cofinitely supplemented if every
submodule N of M with M/N finitely generated has a supplement that is a direct summand of …

Let R be a ring and M a right R‐module. In this note, we show that a quotient of an⊕‐
cofinitely supplemented module is not in general⊕‐cofinitely supplemented and prove that if …

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 …

Let $ R $ be a ring and $ M $ a right $ R $-module. $ M $ is called $\oplus $-cofinitely
supplemented if every submodule $ N $ of $ M $ with $\frac {M}{N} $ finitely generated has 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 …

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 …

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 …

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 …