Journal of the Mathematical Society of Japan

Stickelberger ideals of conductor p and their application

Humio ICHIMURA and Hiroki SUMIDA-TAKAHASHI

Full-text: Open access

Abstract

Let p be an odd prime number and F a number field. Let K = F ( ζ p ) and Δ = G a l ( K / F ) . Let 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 𝒮 Δ annihilates the p -ideal class group of K . In this paper, we study some properties of the ideal 𝒮 Δ ,and check whether or not a subfield of Q ( ζ p ) satisfies the above property.

Article information

Source
J. Math. Soc. Japan, Volume 58, Number 3 (2006), 885-902.

Dates
First available in Project Euclid: 23 August 2006

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1156342042

Digital Object Identifier
doi:10.2969/jmsj/1156342042

Mathematical Reviews number (MathSciNet)
MR2254415

Zentralblatt MATH identifier
1102.11059

Subjects
Primary: 11R18: Cyclotomic extensions 11R33: Integral representations related to algebraic numbers; Galois module structure of rings of integers [See also 20C10]

Keywords
Stickelberger ideal normal integral basis

Citation

ICHIMURA, Humio; SUMIDA-TAKAHASHI, Hiroki. Stickelberger ideals of conductor p and their application. J. Math. Soc. Japan 58 (2006), no. 3, 885--902. doi:10.2969/jmsj/1156342042. https://projecteuclid.org/euclid.jmsj/1156342042


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