Stickelberger ideals of conductor p and their application

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概要

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• Let p be an odd prime number and F a number field. Let K=F(ζp) and Δ=Gal(K/F). Let $¥mathscr{S}$Δ be the Stickelberger ideal of the group ring Z[Δ] defined in the previous paper [8]. As a consequence of a p-integer version of a theorem of McCulloh [15], [16], it follows that F has the Hilbert-Speiser type property for the rings of p-integers of elementary abelian extensions over F of exponent p if and only if the ideal $¥mathscr{S}$Δ annihilates the p-ideal class group of K. In this paper, we study some properties of the ideal $¥mathscr{S}$Δ, and check whether or not a subfield of Q(ζp) satisfies the above property.

• Mathematical Society of Japanの論文
• 2006-07-01

著者

• Sumida-takahashi Hiroki

  Faculty And School Of Engineering The University Of Tokushima

• Ichimura Humio

  Faculty Of Science Ibaraki University

• Sumida Takahashi

  Faculty And School Of Engineering The University Of Tokushima

関連論文

• Hilbert-Speiser number fields and the complex conjugation
• On the 2-part of the class numbers of cyclotomic fields of prime power conductors
• Examples of the Iwasawa invariants and the higher K-groups associated to quadratic fields
• Imaginary quadratic fields satisfying the Hilbert-Speiser type condition for a small prime p
• Stickelberger ideals of conductor p and their application
• On Hilbert-Speiser type imaginary quadratic fields
• Computation of the p-part of the ideal class group of certain real abelian fields

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