  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 uniqueness of inverse series to formal Laurent series. Some necessary and
sufficient conditions for the existence of inverse series to a certain type
formal Laurent series are provided. Moreover, we define a general composition
of formal Laurent series and investigate the Right Distributive Law and the
Chain Rule for formal Laurent series. Finally, we provide a sufficient
condition for the boundary convergence of formal Laurent series.
