In this paper, we give some characterizations of modules M over a ring R such that every
submodule has a unique closure relative to a hereditary torsion theory on Mod-R by using …

We introduce and study a nontrivial generalization of uniserial modules and rings. A module
is called weakly uniserial if its submodules are comparable regarding embedding. Also, a …

Let R be a ring (not necessarily commutative). A left R-module is said to be cotorsion if Ext 1
R (G, M)= 0 for any flat R-module G. It is well known that each pure-injective left R-module is …

Let R be a commutative ring with a nonzero identity and M an R-module. Set ϕ-tor (M)={x∈
M| sx= 0 for some s∈ R∖ Nil (R)}, if ϕ-tor (M)= M then M is called a ϕ-torsion module. An R …

NOTES ON FP-PROJECTIVE MODULES AND FP-INJECTIVE MODULES 1. Introduction
Throughout this paper, all rings are associative with id Page 1 February 17, 2006 17:49 …

Let R be a left and right Noetherian ring. We introduce the notion of the torsionfree
dimension of finitely generated R-modules. For any n 0, we prove that R is a Gorenstein ring …

Injective and projective modules are studied relative to a hereditary torsion theory τ on Mod–
R. It is shown that every τ–projective module is projective if and only if the torsion ideal of R …

An R-module M is called c-retractable if there exists a nonzero homomorphism from M to any
of its nonzero complement submodules. In this paper, we provide some new results of c …

Let X be a left R-module. We characterize when the direct sum of two X-extending modules
is X-extending via essential injectivity and pseudo injectivity of modules. As a corollary, we …

Let C be a semidualizing R-module, where R is a commutative ring. We first introduce the
definition of C-cotorsion modules, and obtain the properties of C-cotorsion modules. As …