Abstract
Several kinds of formal Laurent series have been introduced with some restrictions so far. This paper systematically sets up a natural definition and structure of formal Laurent series without those restrictions, including introducing a multiplication between formal Laurent series. This paper also provides some results on the algebraic structure of the space of formal Laurent series, denoted by \(\mathbb{L}\). By means of the results of the generalized composition of formal power series, we define a composition of a Laurent series with a formal power series and provide a necessary and sufficient condition for the existence of such compositions. The calculus about formal Laurent series is also introduced.
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Gan, XX., Bugajewski, D. On formal Laurent series. Bull Braz Math Soc, New Series 42, 415–437 (2011). https://doi.org/10.1007/s00574-011-0023-6
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DOI: https://doi.org/10.1007/s00574-011-0023-6