We characterize semiperfect modules? semiperfect rings, and perfect rings using locally
projective covers and generalized locally projective covers, where locally projective …

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 …

Let M be a left module over a ring R and I an ideal of R. We call (P, f) a projective I-cover of
M if f is an epimorphism from P to M, P is projective, Kerf⊆ IP, and whenever P= Kerf+ X …

Rings for which all modules have projective covers or for which all finitely generated
modules have projective covers have been studied extensively. These are the perfect and …

In this paper, we study the class of modules having the property that if any pure submodule
is isomorphic to a direct summand of such a module then the pure submodule is itself a …

We prove the following results for a ring R.(a) If C is a class of right R-modules closed under
direct summands and isomorphisms, then every right R-module has an epic C-envelope if …

In the seminal paper [1], Bass provided a number of characterizations of left perfect rings. In
the course of the proof of his" Theorem P", Bass implicitly showed that the ring R is left …

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 …

When every projective module is a direct sum of finitely generated modules Page 1 Journal
of Algebra 315 (2007) 454–481 www.elsevier.com/locate/jalgebra When every projective …

We introduce nets in rings, which turn out to describe right flat modules and left flat modules
over a fixed ring R at the same time. As an application we prove that for a finitely generated …