Hilbert-Speiser number fields and Stickelberger ideals

DOI10.5802/jtnb.690zbMath1205.11119OpenAlexW2057961848MaRDI QIDQ988066

Humio Ichimura

Publication date: 25 August 2010

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_2009__21_3_589_0

zbMATH Keywords

normal integral basisStickelberger ideal

Mathematics Subject Classification ID

Cyclotomic extensions (11R18) Integral representations related to algebraic numbers; Galois module structure of rings of integers (11R33)

Related Items

Biographical Sketch of Professor Humio Ichimura

Cites Work

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• On the ring of \(p\)-integers of a cyclic \(p\)-extension over a number field
• A class number formula for the \(p\)-cyclotomic field
• \(\mathbb Z_p\)-extensions of complex multiplication fields
• Hilbert-Speiser number fields for a prime \(p\) inside the \(p\)-cyclotomic field
• On the Stickelberger ideal and the circular units of an abelian field
• Class numbers and \(\mathbb Z_p\)-extensions
• The non-p-part of the class number in a cyclotomic \(\mathbb{Z}_p\)-extension
• Cyclic Galois extensions of commutative rings
• Normal integral bases in Kummer extensions of prime degree
• On the ring of integers of a tame Kummer extension over a number field.
• Galois module structure of elementary abelian extensions
• Stickelberger ideals of conductor \(p\) and their application
• Normal integral bases for cyclic Kummer extensions
• Ideal Class Groups of Iwasawa-Theoretical Abelian Extensions Over the Rational Field
• On the parity of the class number of the 7nth cyclotomic field
• Galois module structure of abelian extensions.
• Class Number Computations of Real Abelian Number Fields
• Euler Systems