Cotorsion modules for torsion theories
Henderson, J., Orzech, M. (1977)
Portugaliae mathematica
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Cotorsion modules for torsion theories
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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...