In this paper we prove that any sheaf of modules over any topological space (in fact, any
$\mathcal {O} $-module where $\mathcal {O} $ is a sheaf of rings on the topological space) …

The study of flat covers and cotorsion envelopes has turned out to be very useful since their
existence was proved in [3] for the category of R-modules. The problem is even more …

Introduction. The natural setting for a theory of sheaves is a site, iea category C topologized
in the sense of Grothendieck(cf. VERDIER[1963]). We shall consider a sheaf A of rings on a …

In this paper, we prove the existence of a flat cover and of a cotorsion envelope for any quasi-
coherent sheaf over a scheme (X, OX). Indeed we prove something more general. We define …

In this paper we initiate a study of the theory of cosheaves of modules. We are interested
mainly in those facts which are not encompassed by the known theories of sheaves with …

A note on flasque sheaves Page 1 BULL. AUSTRAL. MATH. SOC. MOS 1405, 1455 VOL. 2 (1970),
229-232. A note on flasque sheaves JM Campbell We give an elementary and self-contained …

It is not known whether modules over an arbitrary ring have flat covers, however for certain
modules over commutative noetherian rings they can be shown to exist. These covers, in …

A morphism f: M→ N of left R-modules is a phantom morphism if for any morphism g: A→ M,
with A finitely presented, the composition fg factors through a projective module …

We show that if a class of modules is closed under pure quotients, then it is precovering if
and only if it is covering, and this happens if and only if it is closed under direct sums. This is …

In this paper we prove the existence of a flat cover and a cotorsion envelope for any quasi-
coherent sheaf over the projective line, where R is any commutative ring. We first prove a …