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Irreducibility in generalized power series (2405.13815v1)
Published 22 May 2024 in math.AC
Abstract: A classical tool in the study of real closed fields are the fields $K((G))$ of generalized 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 $G$. In this paper we enlarge the family of ordinals $\alpha$ of non-additively principal Cantor degree for which $K((\mathbb{R}{\le 0}))$ admits irreducibles of order type $\alpha$ far beyond $\alpha=\omega2 $ and $\alpha = \omega3$ known prior to this work.