Abstract
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-Sigma-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.