Jrg. Rozas et B. Torrecillas, ON THE EXISTENCE OF COVERS BY INJECTIVE-MODULES RELATIVE TO A TORSIONTHEORY, Communications in algebra, 24(5), 1996, pp. 1737-1748
Let R be a ring with identity. In this note we study covers of left R-
modules by tau-injectives left R-modules, where tau is a hereditary to
rsion theory defined in the category of all left R-modules and all R-m
orphisms. When R is an artinian commutative ring, a complete answer ab
out the existence of such covers for every R-module is given. In case
that tau is a centrally splitting torsion theory, we can characterize
those tau for which every left R-module has a tau-injective cover. Als
o we analyze R-modules such that the injective and the tau-injective c
over are the same. At the end of this note we relate the concepts of c
olocalization and cover.