HOUSTON JOURNAL OF MATHEMATICS, cilt.39, sa.2, ss.343-362, 2013 (SCI-Expanded)
In the first part of this paper, we prove the existence of torsion free covers in the category of representations of quivers, (Q; R-Mod), for a wide class of quivers included in the class of the so-called source injective representation quivers provided that any direct sum of torsion free and injective R-modules is injective. In the second part, we prove the existence of F-cw-covers and F-cw(perpendicular to)-envelopes for any quiver Q and any ring R with unity, where F-cw is the class of all "componentwise" flat representations of Q.