  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.

Representation Theory;Rings and Algebras