This paper investigates the structure of cyclically pure (or C-pure) projective modules. In
particular, it is shown that a ring R is left Noetherian if and only if every C-pure projective left …

An R-module F is called closed (neat) projective if, for every closed (neat) submodule L of
every R-module M, every homomorphism from F to M/L lifts to M. In this paper, we study …

In this paper, we introduce and study the pure-direct-projective modules, that is the modules
M every pure submodule A of which with M/A isomorphic to a direct summand of M is a direct …

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 …

A famous theorem of algebra due to Osofsky states that “if every cyclic left R-module is
injective, then R is semisimple”. Therefore, a natural question of this sort is:“What is the class …

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) …

In this article, several characterizations of certain classes of rings via FC-purity and I-purity
are considered. Among others results, it is shown that every I-pure injective left R-module is …

In this paper, we introduce and study the dual notion of simple-direct-injective modules.
Namely, a right R-module M is called simple-direct-projective if, whenever A and B are …

R -PROJECTIVE MODULES OVER A SEMIPERFECT RING Page 1 Canad. Math. Bull. Vol. 24
(3), 1981 R -PROJECTIVE MODULES OVER A SEMIPERFECT RING BY RD KETKAR AND N …

A ring R is said to be left pure-hereditary (resp. RD-hereditary) if every left ideal of R is pure-
projective (resp. RD-projective). In this paper, some properties and examples of these rings …