I. Kaplansky has proved that if a torsion free module (over a complete DVR) is countably generated and does not contains infinitely divisible elements then it is free.
Is there any analog of this result for modules over an arbitrary DVR?
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1$\begingroup$ Read the answers at mathoverflow.net/questions/302007/… $\endgroup$– Wilberd van der KallenCommented Jul 10, 2018 at 7:44
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