Swan modules and Hilbert-Speiser number fields

DOI10.1006/jnth.1999.2425zbMath0941.11044OpenAlexW2036653607WikidataQ56455203 ScholiaQ56455203MaRDI QIDQ1961097

Karl Rubin, Anupam Srivastav, Daniel R. Replogle, Cornelius Greither

Publication date: 2 March 2000

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jnth.1999.2425

zbMATH Keywords

Mayer-Vietoris sequenceStickelberger idealSwan subgroupHilbert-Speiser propertytamely ramified abelian extension

Mathematics Subject Classification ID

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

Related Items (25)

On Hilbert-Speiser fields ⋮ Indices of Kummer extensions of prime degree ⋮ Kernel groups and nontrivial Galois module structure of imaginary quadratic fields ⋮ Real abelian fields satisfying the Hilbert-Speiser condition for some small primes \(p\) ⋮ Nontrivial Galois module structure of cyclotomic fields ⋮ Abelian number fields satisfying the Hilbert-Speiser condition at \(p=2\) or \(3\) ⋮ On the restricted Hilbert-Speiser and Leopoldt properties ⋮ Normal integral bases for cyclic Kummer extensions ⋮ Relative normal bases of positive characteristic ⋮ Normal integral bases and strict ray class groups modulo 4 ⋮ Relative Galois module structure of rings of integers of absolutely abelian number fields ⋮ On the ring of integers of a tame Kummer extension over a number field. ⋮ Note on imaginary quadratic fields satisfying the Hilbert-Speiser condition at a prime \(p\) ⋮ Cyclotomic Swan subgroups and primitive roots. ⋮ Sequences of Hopf-Swan subgroups. ⋮ Computation of several cyclotomic Swan subgroups ⋮ Tame Galois module structure revisited ⋮ On a theorem of Kawamoto on normal bases of rings of integers ⋮ Hilbert-Speiser number fields and the complex conjugation ⋮ Cyclotomic Swan subgroups and irregular indices ⋮ Note on the ring of integers of a Kummer extension of prime degree. IV ⋮ Note on the rings of integers of certain tame 2-Galois extensions over a number field ⋮ Swan modules and realisable classes for Kummer extensions of prime degree ⋮ On the self-duality of rings of integers in tame and abelian extensions ⋮ Note on the ring of integers of a Kummer extension of prime degree. V.

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