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ABSTRACT
The notion of an almost -precover as a generalization of a
-precover is introduced. Among other results it is shown that if
is any hereditary torsion theory for the category R-mod, then every module has an almost
-torsionfree precover and an almost Coprod(
)-precover, where
denotes the class all
-torsionfree
-injective modules. Especially, every module has an almost Coprod(
)-precover, where
is the class of all injective modules.
ACKNOWLEDGMENTS
This work has been initiated while the first author was visiting the University of Almería.
The first author has been partially supported by the Grant Agency of the Charles University, grant #GAUK 169/1999/B - MAT/MFF and also by the institutional grant MSM 113 200 007.
The second author has been partially supported by PB98-1005 from DGES.