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!



Question about modules, quotient rings, and polynomial rings?
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.


