Abstract
Given a complete Serre class τ this determines a torsion theory with T the class of torsion modules. It also determines the torsion free modules. For the classical torsion in the category of abelian groups the torsion free modules are flat and visa-versa. Which rings are characterized by this property? More precisely: Which rings admit a torsion theory for which the concepts of torsion free and flat are equivalent? We also dispose of the cases when R admits a toision theory for which torsion free is equivalent to injective and when projective is equivalent to torsion free.
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