The inverse and the composition in the set of formal Laurent series

The aim of this article is to investigate the issues of multiplicative inverses and composition in the set of formal Laurent series. We show the lack of general uniqueness of inverses of formal Laurent series; necessary and sufficient conditions for the existence of inverses of formal Laurent series satisfying some weak assumptions are also provided. Moreover, we define a general composition of formal Laurent series and investigate the Right Distributive Law and the Chain Rule in this context.