Submission date: 15 December 2015

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 in [Berarducci2000] ensures the existence of irreducible series in the subring K((G^{≤ 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 of the ring 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.

Mathematics Subject Classification: Primary 13F25, secondary 03E10, 12J15, 06F25

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Full text arXiv 1512.04895: pdf, ps.