%0 Journal Article
%T Approximations and locally free modules
%A Alexander Slavik
%A Jan Trlifaj
%J Mathematics
%D 2012
%I arXiv
%R 10.1112/blms/bdt069
%X 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.
%U http://arxiv.org/abs/1210.7097v1