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Precovers. (English) Zbl 1016.16003
Summary: Let $$\mathcal G$$ be an abstract class (closed under isomorphic copies) of left $$R$$-modules. In the first part of the paper some sufficient conditions under which $$\mathcal G$$ is a precover class are given. The next section studies the $$\mathcal G$$-precovers which are $$\mathcal G$$-covers. In the final part the results obtained are applied to the hereditary torsion theories on the category of left $$R$$-modules. Especially, several sufficient conditions for the existence of $$\sigma$$-torsionfree and $$\sigma$$-torsionfree $$\sigma$$-injective covers are presented.

##### MSC:
 16D90 Module categories in associative algebras 16S90 Torsion theories; radicals on module categories (associative algebraic aspects) 16D50 Injective modules, self-injective associative rings
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##### References:
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