Lengths of Roots of Polynomials in a Hahn Field

Autor:	K. Lange, Julia F. Knight
Rok vydání:	2021
Předmět:	Properties of polynomial roots Pure mathematics Logic Limit ordinal Field (mathematics) Algebraically closed field Algebra over a field Abelian group Analysis Mathematics
Zdroj:	Algebra and Logic. 60:95-107
ISSN:	1573-8302 0002-5232
DOI:	10.1007/s10469-021-09632-0
Popis:	Let K be an algebraically closed field of characteristic 0, and let G be a divisible ordered Abelian group. Maclane [Bull. Am. Math. Soc., 45, 888-890 (1939)] showed that the Hahn field K((G)) is algebraically closed. Our goal is to bound the lengths of roots of a polynomial p(x) over K((G)) in terms of the lengths of its coefficients. The main result of the paper says that if 𝛾 is a limit ordinal greater than the lengths of all of the coefficients, then the roots all have length less than ωω𝛾.
Databáze:	OpenAIRE
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