The aim of this paper is to study a property of a special kind of exact functors and give some
applications to projective modules and injective modules. In section 1 we introduce the …

By a well known theorem of K. Morita, any equivalence between full module categories over
rings R and S, are given by a bimodule RPS, such that RP is a finitely generated projective …

We consider an arbitrary Abelian category A and a subcategory T closed under extensions
and direct summands, and characterize those T that are (semi-) special preenveloping in A; …

In this paper, we develop relative homological algebra in the category of functors from
finitely presented modules to Abelian groups. More specifically, we introduce the concepts of …

Covers and Directed Colimits Page 1 Algebr Represent Theor (2006) 9: 423–430 DOI
10.1007/s10468-006-9030-5 Covers and Directed Colimits Robert El Bashir Received: 1 …

Let $ R $ be a commutative Noetherian ring with non-zero identity, $\fa $ an ideal of $ R $,
and $ X $ an $ R $--module. In this paper, for fixed integers $ s, t $ and a finite $\fa $--torsion …

On splitting of module categories Page 1 Math. Z. t11, 145-150 (1969) On Splitting of Module
Categories HIROYUKI TACHIKAWA Let R be a ring and 9XR the category of all right …

We study finiteness conditions in Grothendieck categories by introducing the concepts of
objects of type FP n and studying their closure properties with respect to short exact …

In the general setting of Grothendieck categories with enough projectives, we prove
theorems that make possible to restrict the study of the problem of the existence of F-covers …

Absolutely pure modules act in ways similar to injective modules. Therefore, through-out this
document we investigate many of these properties of absolutely pure modules which are …