Abstract
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 τ 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 ατ n (R)=τ n (S) where α is the category equivalenceR-Mod→S-Mod. Consequently the localized ringsR τn (R) andS τ n (S) are Morita equivalent.
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Haghany, A. On the torsion theories of Morita equivalent rings. Period Math Hung 32, 193–197 (1996). https://doi.org/10.1007/BF02109788
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DOI: https://doi.org/10.1007/BF02109788