An exact sequence 0→ A→ B→ C→ 0 of left R-modules is called cyclically pure if for every
right ideal I of R, the sequence 0→(R/I)⊗ A→(R/I)⊗ B→(R/I)⊗ C→ 0 is exact. In this paper …

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 …

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 …

A SIMPLE RING OVER WHICH PROPER CYCLICS ARE CONTINUOUS IS A PCI-RING Page
1 Canad. Math. Bull. Vol. 41 (3), 1998 pp. 261–266 A SIMPLE RING OVER WHICH PROPER …

PM Cohn [3] has introduced the notion of purity for R-modules. With respect to purity, flat,
absolutely pure and regular modules are studied. In this paper we introduce and study the …

A module satisfying the descending chain condition on cyclic submodules is called
coperfect. The class of coperfect modules lies properly between the class of locally artinian …

A ring R is called right PCI if every proper cyclic right R-module is injective, ie if C is a cyclic
right R-module then CR≅ RR or CR is injective. By [2] and [3], if R is a non-artinian right PCI …

Let C be a class of some finitely presented left R-modules. A left R-module M is called C-
injective, if Ext R 1 (C, M)= 0 for each C∈ C. A right R-module M is called C-flat, if Tor 1 R …

In this paper, we obtain the structure of the endomorphism rings of nonsingular semiperfect
progenerator uniform CS modules with uniform submodule. It is shown that such rings are …

We investigate the structure of pure-syzygy modules in a pure-projective resolution of any
right R-module over an associative ring R with an identity element. We show that a right R …