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May 14, 2022 at 4:39 comment added Chen @PiotrAchinger Thanks I have added the condition that $M$ is torsion-free as well.
May 14, 2022 at 4:38 history edited Chen CC BY-SA 4.0
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May 13, 2022 at 19:49 comment added Piotr Achinger What happens when $M=R/(f)$? Then it is torsion free mod $f$, but $M/gM = R/(f,g)$ is unlikely to be torsion free over $R/(g)$ if $(g)\neq (f)$.
May 13, 2022 at 18:08 history asked Chen CC BY-SA 4.0