A module is called locally pure-projective if every pure epimor-phism onto it is locally split.
We prove that every locally pure-projective module is a Mittag-Leffler module. We derive …

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) …

Let M be a left module, over a ring R. M is called a Zelmanowitz-regular module if for each
x∊ M there exists a homomorphism f: M→ R such that f (x) x= x. Let Q be a left R-module and …

In this paper we prove that every Mittag-Leffler module is a pure submodule of a reduced
product of pure-projective modules. This leads us to look for characterizations of the rings …

In a recent paper, Holston et al. have defined a module M to be N-subprojective if for every
epimorphism g: B→ N and homomorphism f: M→ N, there exists a homomorphism h: M→ B …

Let M be a left module over a ring R. A submodule N of M is called locally split in M if for
each x EN there exists a homomorphism h: Mt N such that h (x)= x. It is shown that if N is …

The subject of this article are the modules M over a ring R such that every element of M is
contained in a pure-injective direct summand of M. For obvious reasons we call these …

Given a module M over a ring R, G. Azumaya [1] introduced the dual notions of M-projective
and M-injective modules. These concepts have actually led MS Shrikhande to a study of …

ABSTRACT A module M Is said to be weakly projective If and only If It has a projective cover
11": P (M)--+ M and every map from P (M) Into a finitely generated (free) module can be …

We approach the analysis of the extent of the projectivity of modules from a fresh perspective
as we introduce the notion of relative subprojectivity. A module M is said to be N …