Irreducibility in generalized power series
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916257388822528 |
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| author | Fornasiero, Antongiulio Lavi, Noa L'Innocente, Sonia Mantova, Vincenzo |
| author_facet | Fornasiero, Antongiulio Lavi, Noa L'Innocente, Sonia Mantova, Vincenzo |
| contents | 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 $α$ of non-additively principal Cantor degree for which $K((\mathbb{R}^{\le 0}))$ admits irreducibles of order type $α$ far beyond $α=ω^2 $ and $α= ω^3$ known prior to this work. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_13815 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Irreducibility in generalized power series Fornasiero, Antongiulio Lavi, Noa L'Innocente, Sonia Mantova, Vincenzo Commutative Algebra 13F25, 13F15 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 $α$ of non-additively principal Cantor degree for which $K((\mathbb{R}^{\le 0}))$ admits irreducibles of order type $α$ far beyond $α=ω^2 $ and $α= ω^3$ known prior to this work. |
| title | Irreducibility in generalized power series |
| topic | Commutative Algebra 13F25, 13F15 |
| url | https://arxiv.org/abs/2405.13815 |