Some Properties of Precovers and Covers

At the beginning of this note the $mathcal{G}$ -covers, $mathcal{G}$ being a hereditary class of modules, are characterized as that for which the homomorphisms into $mathcal{G}$ -precovers are injective as well as that for which the homomorphisms from $mathcal{G}$ -precovers are surjective. The next part studies the (pre)covers of (relatively) injective modules and some relations between the (relative) injectivity of modules and their (pre)covers.