The central aim of this book is to understand modules and the categories they form through
associated structures and dimensions, which reflect the complexity of these, and similar …

In this paper, we study a particular case of Gorenstein projective, injective, and flat modules,
which we call, respectively, strongly Gorenstein projective, injective, and flat modules. These …

Let AA be an abelian category having enough projective objects and enough injective
objects. We prove that if AA admits an additive generating object, then the extension …

The question is addressed of when all pure-projective modules are direct sums of finitely
presented modules. It is proved that this is the case over hereditary noetherian rings. Partial …

A right R-module M is called a D 3-module, if M 1 and M 2 are direct summands of M with M=
M 1+ M 2, then M 1∩ M 2 is a direct summand of M. Following the work of Bass on projective …

When every projective module is a direct sum of finitely generated modules Page 1 Journal
of Algebra 315 (2007) 454–481 www.elsevier.com/locate/jalgebra When every projective …

Let R be a ring. A right R-module C is called a cotorsion module if Ext1R (F, C)= 0 for any flat
right R-module F. In this paper, we first characterize those rings satisfying the condition that …

BV Zabavsky. Fractionally regular Bezout rings, Mat. Stud. 32 (2009), 76 80. It is proved that
a fractionally regular Bezout ring has stable range 3. A PM-ring which is a fractionally …

We show that a strong form (the fully faithful version) of the generating hypothesis,
introduced by Freyd in algebraic topology, holds in the derived category of a ring R if and …

In this article, the projectivity of finitely generated flat modules of a commutative ring are
studied from a topological point of view. Then various interesting results are obtained. For …