References concerning $\mathbb{C}[\partial]$-modules?

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I'm reading the book Vertex algebras for begginers by Victor Kac. From certain point on, the book uses the term $\mathbb{C}[\partial]$-module. It is pretty obvious to me what this means, i.e., a $\mathbb{C}[\partial]$-module is a module over the ring of polynomial expressions on $\partial$.

However I would like to read a formal definition and some general properties, but I haven't found any reference dealing with these modules, neither in my university's library or in the web (everything I have found is a mention in the wikipedia's article about Lie conformal algebras). I would appreaciate some good references concerning these modules.

Thanks in advance.