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arXiv · 1512.04895

Factorisation of germ-like series

Sonia L'Innocente·Vincenzo Mantova
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Abstract

A classical tool in the study of real closed fields are the fields $K((G))$ of generalised power series (i.e., formal sums with well-ordered support) with coefficients in a field $K$ of characteristic 0 and exponents in an ordered abelian group $G$. A fundamental result of Berarducci ensures the existence of irreducible series in the subring $K((G^{\leq 0}))$ of $K((G))$ consisting of the generalised power series with non-positive exponents. It is an open question whether the factorisations of a series in such subring have common refinements, and whether the factorisation becomes unique after taking the quotient by the ideal generated by the non-constant monomials. In this paper, we provide a new class of irreducibles and prove some further cases of uniqueness of the factorisation.

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Sonia L'Innocente, Vincenzo Mantova. 2017-04-20. Factorisation of germ-like series. https://doi.org/10.4115/jla.2017.9.3

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