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In the a-adic topology, if M,N are A-modules, and N is the homomorphic image of M, can we prove that N is complete whenever M is? in other words, does completeness carries over to homomorphic images.

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    $\begingroup$ This is clear if $A$ is Noetherian and $M$ and $N$ are finitely generated, so presumably you are thinking of some more general context. Are you willing to assume any finiteness conditions at all? $\endgroup$
    – Neil Strickland
    Commented Apr 20, 2013 at 20:10

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