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 …

Let R be a ring. A collection of R-modules containing the zero module and closed under
isomorphisms will be denoted by X. An R-module M is said to be X-lifting if for every X …

In this work, FZ-hollow and Z-semihollow modules are defined as a generalization of F-
hollow and semihollow modules, and some properties of these concepts of modules are …

A module M over a ring R is called hollow-lifting if every submodule N of M with M/N hollow
contains a direct summand K of M such that N/K is a small submodule of M/K. It is known that …

Let U be a submodule of a module M. We call U a strongly lifting submodule of M if
whenever M/U=(A+ U)/U⊕(B+ U)/U, then M= P⊕ Q such that P≤ A,(A+ U)/U=(P+ U)/U and …

If R is a right coherent ring, then left R-modules have covers by submodules of flat R-
modules if and only if all injective left R-modules have flat covers. This is the case if R is …

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 …

The aim of this note is to characterize right perfect rings using€ 9–supplemented modules.
Let R be a ring. We prove that R is a right perfect ring if and only if every T-projective right R …

arXiv:1312.4023v1 [math.RA] 14 Dec 2013 Page 1 arXiv:1312.4023v1 [math.RA] 14 Dec 2013
ON A CLASS OF LIFTING MODULES HATICE INANKIL, SAIT HALICIOGLU, AND ABDULLAH …