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We generalize the well-known fact that for a pair of Morita equivalent rings $R$ and $S$ their maximal rings of quotients are again Morita equivalent: If $\tau_n (M)$ denotes the torsion theory cogenerated by the direct sum of the first $n+1$ injective modules forming part of the minimal injective resolution of $M$ then $\alpha \tau_n(R)=\tau_n (S)$ where $\alpha$ is the category equivalence $R$-Mod$\longrightarrow S$-Mod. Consequently the localized rings $R_{\tau_n (R)}$ and $S_{\tau_n (S)}$ are Morita equivalent.
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