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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.

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    $\begingroup$ I vote to close this question, as it is not a research-level question, and thus not on-topic for this site. There is however a similiar site, math.stackexchenge.com with a broader scope where such a question would be welcome. For detailse please see the FAQs. $\endgroup$
    – user9072
    Commented Sep 18, 2011 at 11:07

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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.

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    $\begingroup$ Of course this is a correct answer, but such answers probably support these questions (which are offtopic, as quid already mentioned). $\endgroup$
    – Martin Brandenburg
    Commented Sep 18, 2011 at 11:14

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