I'm not really a mathematician, and looking for some literature which could potentially help me in research. Im interested in algebra of rational functions (ratios of polynomials) of finite order.
Specifically, I'm trying to study classes / families of rational functions that could be used as a basis under addition for all rational functions of a certain order.
Which branch of algebra should I turn to? It's very hard to Google this. Does this even exist as a field of study?
If this is in some sense vague or nonsensical, please ask for specific clarifications.