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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.

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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