If $G$ is a module over the non-trivial commutative Noetherian ring $R$ then is it possible that for all maximal ideal $M$ of $R$ we have $MG=G$ ?
I guess the answer is no.
If $G$ is a module over the non-trivial commutative Noetherian ring $R$ then is it possible that for all maximal ideal $M$ of $R$ we have $MG=G$ ?
I guess the answer is no.
Actually the answer is yes: $R=\mathbb Z, G=\mathbb Q$ .