MODULES SATISFYING THE ASCENDING CHAIN CONDITION ON SUBMODULES WITH A
BOUNDED NUMBER OF GENERATORS Patrick F. Smith All rings ha Page 1 International …

We study the notions of n-hereditary rings and its connection to the classes of finitely n-
presented modules, FP n-injective modules, FP n-flat modules and n-coherent rings. We …

Let R be a ring. A subclass T of left R-modules is called a weak torsion class if it is closed
under homomorphic images and extensions. Let T be a weak torsion class of left R-modules …

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 …

We investigate modules M having the injective property relative to nonsingular modules.
Such modules are called “N-injective modules”. It is shown that M is an N-injective R-module …

An R-module M is called weakly co-Hopfian if any injective endomorphism of M is essential.
The class of weakly co-Hopfian modules lies properly between the class of co-Hopfian and …

An R-module M is called strongly FP-injective if Ext R i (P, M)= 0 for any finitely presented R-
module P and any i> 0. Denoted by SFI the class of all strongly FP-injective R-modules and …

Abstract A right R-module M is called coretractable (s-coretractable) if Hom (M/K, M) ≠ 0
Hom (M/K, M)≠ 0 for any proper submodule (supplement submodule) K of M. In this article …

A ring extension is a ring homomorphism preserving identities. In this paper, we give the
definition of relatively free modules on ring extensions and develop some basic properties of …

Let N be a left R-module with the endomorphism ring S= End (RN). Given two cardinal
numbers α and β and a matrix A∈ S β× α, N is called flat relative to A in case, for each x∈ lN …