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arXiv · 1210.7097

Approximations and locally free modules

Alexander Slavik·Jan Trlifaj
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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-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.

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BibTeXRIS

Alexander Slavik, Jan Trlifaj. 2012-10-26. Approximations and locally free modules. https://doi.org/10.1112/blms%2Fbdt069

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