Open Access
July, 2006 Stickelberger ideals of conductor p and their application
J. Math. Soc. Japan 58(3): 885-902 (July, 2006). DOI: 10.2969/jmsj/1156342042


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.


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Humio ICHIMURA. Hiroki SUMIDA-TAKAHASHI. "Stickelberger ideals of conductor p and their application." J. Math. Soc. Japan 58 (3) 885 - 902, July, 2006.


Published: July, 2006
First available in Project Euclid: 23 August 2006

zbMATH: 1102.11059
MathSciNet: MR2254415
Digital Object Identifier: 10.2969/jmsj/1156342042

Primary: 11R18 , 11R33

Keywords: normal integral basis , Stickelberger ideal

Rights: Copyright © 2006 Mathematical Society of Japan

Vol.58 • No. 3 • July, 2006
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