Approximations and locally free modules
  For any set of modules S, we prove the existence of precovers (right approximations) for all classes of modules of bounded C-resolution dimension, where C is the class of all S-filtered modules. In contrast, we use infinite dimensional tilting theory to show that the class of all locally free modules induced by a non-sum-pure-split tilting module is not precovering. Consequently, the class of all locally Baer modules is not precovering for any countable hereditary artin algebra of infinite representation type. 
Alexander Slavik and Jan Trlifaj
math.RT math.RA