If $A/B \cong C/B$, then is it true that $A\cong C$?

Question

Let $A, B$ and $C$ be $R$- submodules of an $R$- module $M$ and $A/B \cong C/B$. Then is it true that $A\cong C$? Here $B$ is a submodule of both $A$ and $C$.

What do you think? What have you tried? – Ove Ahlman Dec 07 '17 at 08:14 — Ove Ahlman, Dec 07 '17 at 08:14

score 2 · Accepted Answer · answered Dec 08 '17 at 13:08

2

Consider the copy of $\mathbb Z/2$ that sits inside $\mathbb Z/2 \oplus \mathbb Z/2$ and inside $\mathbb Z/4$.

answered Dec 08 '17 at 13:08

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If $A/B \cong C/B$, then is it true that $A\cong C$?

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