Pólya fields, Pólya groups and Pólya extensions: a question of capitulation

DOI10.5802/jtnb.758zbMath1282.13040OpenAlexW2323872112MaRDI QIDQ449703

Amandine Leriche

Publication date: 31 August 2012

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=JTNB_2011__23_1_235_0/

zbMATH Keywords

regular basisintegral-valued polynomialsPólya extensionPólya field

Mathematics Subject Classification ID

Galois theory (11R32) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Class field theory (11R37) Polynomials (irreducibility, etc.) (11R09) Algebraic numbers; rings of algebraic integers (11R04)

Related Items (11)

Class numbers of certain families of totally real biquadratic fields and a result of Mollin ⋮ Some questions on biquadratic Pólya fields ⋮ Pólya groups of the imaginary bicyclic biquadratic number fields ⋮ Cubic, quartic and sextic Pólya fields ⋮ On the Pólya Group of Some Imaginary Biquadratic Fields ⋮ An overview of some recent developments on integer-valued polynomials: Answers and Questions ⋮ Pólya fields and Pólya numbers ⋮ About the embedding of a number field in a Pólya field ⋮ From Pólya fields to Pólya groups. I: Galois extensions ⋮ A survey on fixed divisors ⋮ Relative Pólya group and Pólya dihedral extensions of \(\mathbb{Q}\)

Cites Work

• Generalized factorials and fixed divisors over subsets of a Dedekind domain
• Integer valued polynomials over a number field
• Big projective modules are free
• Integer-Valued Polynomials
• P-orderings and polynomial functions on arbitrary subsets of Dedekind rings.
• Classical theory of algebraic numbers
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