Let R be a commutative ring with 1, and M a unitary right R-module. It is known that if M is a
finitely generated (fg) orjective module, then M* is a fg Projective left R-module and M** is a …

Let $ R $ be a ring and $ M $ a right $ R $-module. We call $ M $, coretractable relative to
$\overline {Z}(M) $(for short, $\overline {Z}(M) $-coretractable) provided that, for every proper …

A module M is said to be weakly N-projective if it has a projective cover π: P (M)↠ M and for
each homomorphism: P (M)→ N there exists an epimorphism σ: P (M)↠ M such that (kerσ) …

We give a criterion for when idempotents of a ring R which commute modulo the Jacobson
radical J (R) can be lifted to commuting idempotents of R. If such lifting is possible, we give …

An R-module M is called∑-extending if every coproduct of copies of M is extending, ie
closed submodules are direct summands. Oshiro (1984) has shown that the ring R is∑ …

Let R be a commutative ring with identity. It often happens that M 1⊕⋯⊕ Ms≅ N 1⊕⋯⊕ Nt
for indecomposable R-modules M 1,…, Ms and N 1,…, Nt with s≠ t. This behavior can be …

Abstract A right R-module M is virtually extending (or CIS) if every complement submodule of
M is isomorphic to a direct summand of M, and M is called a virtually C2-module if every …

The notion of projection invariant subgroups was first introduced by Fuchs in [7]. We will
define the module-theoretic version of the projection invariant subgroup. Let R be a ring and …

An R-module M is called an extending module, and also called CS, if it satisfies the following
full extending property: For any submodule X of M, there exists a direct summand X∗ of M …

Generalizing concepts “right Bezout” and “principal right ideal” of a ring R to modules, an R-
module M is called n-epiretractable (resp. epi-retractable) if every n-generated submodule …