# Question about modules, quotient rings, and polynomial rings? [closed]

Consider an integer polynomial ring, $A = \mathbb{Z}[t]$, and a ring of fractions, $B = \mathbb{Z}[t, t^{-1}]$; obviously, $A$ is a subring of $B$.

Now we consider two modules over $A$ and $B$, $M$ and $N$. We want to construct a map from $N$ to $M$. But the question is that the two modules are not over the same polynomial ring. So how can we make it?

Great thanks!

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## closed as not a real question by Felipe Voloch, J.C. Ottem, Kevin Walker, quid, Andreas BlassSep 17 '11 at 15:33

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

Please see the FAQ mathoverflow.net/faq for a list of sites where your question would be probably more appropriate. – user2035 Sep 17 '11 at 10:00
Have you tried to apply the "change of ring" technique ? For it, one uses a ring homomorphism $\varphi: R \to S$ and considers a $S$-Module $N$ as $R$-module in the obvious way. If $M$ is a $R$-module, then look for $R$-module homomorphisms $M \to N$. In your example $\varphi$ can be taken to be the inclusion $A \hookrightarrow B$. – Todd Leason Sep 17 '11 at 12:29
I doubt that there is any site where this question would be appropriate. – Steven Landsburg Sep 17 '11 at 13:43

I do not think you can map a module over a smaller ring into a module over a larger ring in this case.$\phi(rx)=r\phi(x)$ will not satisfy.