Show that : every homomorphic image of a Dedekind module is again Dedekind.
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Expert's answer
2013-02-18T11:47:14-0500
If M is Dedekind module thenfor any submodule N of M we have N*N' = M, where N' =(M:N) in RT^-1, and T={t - non zero divisor, that tm=0 implies m=0}. If we take any K - submodule of M then submodules in M/K are only submodules N that contain K. But property N*N' = M will be preserved since K c M and (M:K) c (M:N).
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