Nontrivial Galois module structure of cyclotomic fields

DOI10.1090/S0025-5718-02-01457-6zbMath1020.11070arXivmath/0201322OpenAlexW2060495462MaRDI QIDQ4794648

Daniel R. Replogle, Marc Conrad

Publication date: 19 February 2003

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0201322

zbMATH Keywords

unitsnormal integral basiscyclotomic unitsGalois modules

Mathematics Subject Classification ID

Units and factorization (11R27) Class numbers, class groups, discriminants (11R29) Cyclotomic extensions (11R18) Integral representations related to algebraic numbers; Galois module structure of rings of integers (11R33)

Related Items (max. 100)

On Hilbert-Speiser fields ⋮ Kernel groups and nontrivial Galois module structure of imaginary quadratic fields ⋮ Cyclotomic Swan subgroups and primitive roots. ⋮ Note on the rings of integers of certain tame 2-Galois extensions over a number field

Uses Software

• SIMATH

Cites Work

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• Nontrivial lower bounds for class groups of integral group rings
• On the Stickelberger ideal and the circular units of a cyclotomic field
• Swan modules and realisable classes for Kummer extensions of prime degree
• Galois module structure of elementary abelian extensions
• A Mayer-Vietoris sequence for class groups
• Swan modules and Hilbert-Speiser number fields
• Construction of bases for the group of cyclotomic units
• Computation of several cyclotomic Swan subgroups
• On Integral Bases
• Galois module structure of abelian extensions.
• Relative Galois module structure of rings of integers of cyclomatic fields.
• Nontrivial tame extensions over Hopf orders
• Cyclotomic Swan subgroups and irregular indices

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