Geodesic
Precovers
Czechoslovak Mathematical Journal, Tome 53 (2003) no. 1, pp. 191-203

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Let $\mathcal G$ be an abstract class (closed under isomorpic 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 on left $R$-modules. Especially, several sufficient conditions for the existence of $\sigma $-torsionfree and $\sigma $-torsionfree $\sigma $-injective covers are presented.
Classification : 16D50, 16D90, 16S90
Keywords: precover; cover; (pre)cover class of modules; hereditary torsion theory; relatively injective modules 
@article{CMJ_2003__53_1_a14,
     author = {Bican, Ladislav and Torrecillas, Blas},
     title = {Precovers},
     journal = {Czechoslovak Mathematical Journal},
     pages = {191--203},
     publisher = {mathdoc},
     volume = {53},
     number = {1},
     year = {2003},
     mrnumber = {1962008},
     zbl = {1016.16003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2003__53_1_a14/}
}
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Bican, Ladislav; Torrecillas, Blas. Precovers. Czechoslovak Mathematical Journal, Tome 53 (2003) no. 1, pp. 191-203. http://geodesic.mathdoc.fr/item/CMJ_2003__53_1_a14/