Can we view a module over the ring $\mathbb{Q}[t,t^{-1}]$ to be a module over the polynomial ring $\mathbb{Q}[t]$? 


where $\mathbb{Q}$ denote any rational number coefficients. 



How to consider a module over the ring Q[t,t^(-1)] to be a module over the polynomial ring Q[t]?
Yes, via the natural inclusion $\mathbb{Q}[t] \to \mathbb{Q}[t,t^{-1}]$: let an element of $\mathbb{Q}[t]$ act the way it does when considering it as an element of $\mathbb{Q}[t,t^{-1}]$. More generally, if you have a $B$-module $M$ and a morphisms of rings $A \to B$, then you can see $M$ as an $A$-module.


