A question on modules over Noetherian ring

Question

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.

I assume you also want the assumption that $G\neq 0$? – Ben Blum-Smith Jun 23 '12 at 19:50 — Ben Blum-Smith, Jun 23 '12 at 19:50

score 4 · Accepted Answer · answered Jun 23 '12 at 19:50

4

Actually the answer is yes: $R=\mathbb Z, G=\mathbb Q$ .

answered Jun 23 '12 at 19:50

Georges Elencwajg

1 Answers1