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Let $A$ be a commutative ring, $M$ an $A-$module and $U,V,V'$ submodules of $M$ such that $U \cap V = U \cap V'$ and $U+V=U+V'$. Does it follow that $V=V'$?

The answer is no because the condition that $V \subset V'$ is necessary though I can't find a counterexample.

Does someone has a good counterexample for this wrong statement?

Thanks in advance!

Cheers,

Siron