1. Irreducibility in generalized power series
- Author
-
Fornasiero, Antongiulio, Lavi, Noa, L'Innocente, Sonia, and Mantova, Vincenzo
- Subjects
Mathematics - Commutative Algebra ,13F25, 13F15 - 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=\omega^2 $ and $\alpha = \omega^3$ known prior to this work.
- Published
- 2024