On the torsion theories of Morita equivalent rings

We generalize the well-known fact that for a pair of Morita equivalent ringsR andS their maximal rings of quotients are again Morita equivalent: If _n (M) denotes the torsion theory cogenerated by the direct sum of the firstn+1 injective modules forming part of the minimal injective resolution ofM then _n (R)=_n (S) where is the category equivalenceR-ModS-Mod. Consequently the localized ringsR_n(R) andSn_(S) are Morita equivalent.