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On torsionfree classes which are not precover classes

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Abstract

In the class of all exact torsion theories the torsionfree classes are cover (pre-cover) classes if and only if the classes of torsionfree relatively injective modules or relatively exact modules are cover (precover) classes, and this happens exactly if and only if the torsion theory is of finite type. Using the transfinite induction in the second half of the paper a new construction of a torsionfree relatively injective cover of an arbitrary module with respect to Goldie’s torsion theory of finite type is presented.

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Authors and Affiliations

  1. KA MFF UK, Sokolovská 83, 186 00, Praha 8-Karlín, Czech Republic

    Ladislav Bican

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  1. Ladislav Bican
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Correspondence to Ladislav Bican.

Additional information

This research has been partially supported by the Grant Agency of the Czech Republic, grant #GAČR 201/06/0510 and also by the institutional grant MSM 0021620839.

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Bican, L. On torsionfree classes which are not precover classes. Czech Math J 58, 561–568 (2008). https://doi.org/10.1007/s10587-008-0035-6

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  • DOI: https://doi.org/10.1007/s10587-008-0035-6

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