We extend the cotorsion dimension of R-modules to unbounded R-complexes by applying
the flat model structure on Ch (R) proposed by J. Gillespie. This is not natural because there …

In commutative ring theory, the notion of Gorenstein rings has been studied widely. For rings
having finite Krull dimension, Bass showed the characterization of Gorenstein rings as rings …

Let C and D be two classes of left R-modules, l DC= the class of all left R-modules admitting
exact left C-resolutions which are Hom (-, D)-exact, r CD= the class of all left R-modules …

In this paper, we study the class of complexes of FP-injective left R-modules. It is shown that
the pair is a complete cotorsion pair. If R is a left coherent ring, it is proved that every …

In previous papers (Mtiller [11, 12]) we have studied Morita dualities. These are
contravariant category equivalences between categories of right R-modules and left S …

However, some aspects of the classical theory can be extended to infinitely generated
modules over arbitrary rings. In this paper, we will consider such an aspect: the relation of …

If $ R $ is a ring with 1, we call a unital left $ R $-module $ M $ co-Hopfian (Hopfian) in the
category of left $ R $-modules if any monic (epic) endomorphism of $ M $ is an …

The concept of cotorsion was first introduced in the category of Abelian groups (Fuchs [l]).
Matlis [5], studied the cotorsion modules over integral domains. Henderson and Orzech [4] …

Let R be a commutative Cohen–Macaulay ring, and let C be a semidualizing module of R. In
this paper, we show that C is generically dualizing if and only if the tensor products of …

Let C be a semidualizing module for a commutative ring R. It is shown that the-injective
dimension has the ability to detect the regularity of R as well as the-projective dimension. It …