I'm reading a remark in Atiyah, Macdonald - Introduction to Commutative Algebra and I can't really see what is going on.
After giving the definition and a few examples of $R$-Modules (for a ring $R$), the following statement appears:
If $A = k[x]$, where $k$ is a field, then an $A$-module is a $k$-vector space with a linear transformation.
I'm not sure how to "precisify" this statement. Certainly $A$ is a ring in this case so the concept of an $A$-module is well defined.
I'm certainly open to even a vague hint; I think I would benefit from working out the details and I need to rapidly get familiar these ideas.