Geodesic
On torsionfree classes which are not precover classes
Czechoslovak Mathematical Journal, Tome 58 (2008) no. 2, pp. 561-568 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In the class of all exact torsion theories the torsionfree classes are cover (precover) 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.
In the class of all exact torsion theories the torsionfree classes are cover (precover) 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.
Classification : 16D50, 16D90, 16S90, 18E40
Keywords: hereditary torsion theory; exact; noetherian and perfect torsion theory; Goldie’s torsion theory; precover class; cover class; precover and cover of a module 
@article{CMJ_2008_58_2_a18,
     author = {Bican, Ladislav},
     title = {On torsionfree classes which are not precover classes},
     journal = {Czechoslovak Mathematical Journal},
     pages = {561--568},
     year = {2008},
     volume = {58},
     number = {2},
     mrnumber = {2411109},
     zbl = {1166.16013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2008_58_2_a18/}
}
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Bican, Ladislav. On torsionfree classes which are not precover classes. Czechoslovak Mathematical Journal, Tome 58 (2008) no. 2, pp. 561-568. http://geodesic.mathdoc.fr/item/CMJ_2008_58_2_a18/