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Some Properties of Precovers and Covers

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Abstract

At the beginning of this note the \(\mathcal{G}\)-covers, \(\mathcal{G}\) being a hereditary class of modules, are characterized as that for which the homomorphisms into \(\mathcal{G}\)-precovers are injective as well as that for which the homomorphisms from \(\mathcal{G}\)-precovers are surjective. The next part studies the (pre)covers of (relatively) injective modules and some relations between the (relative) injectivity of modules and their (pre)covers.

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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.

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Dedicated to Fred Van Oystaeyen, on the occasion of his sixtieth birthday.

This research has been partially supported by the Grant Agency of the Czech Republic, grant #GAČR 201/06/510 and also by the institutional grant MSM 0021620839.

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Bican, L. Some Properties of Precovers and Covers. Algebr Represent Theor 12, 311–318 (2009). https://doi.org/10.1007/s10468-009-9146-5

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  • DOI: https://doi.org/10.1007/s10468-009-9146-5

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