Swan modules and realisable classes for Kummer extensions of prime degree

DOI10.1006/jabr.1998.7652zbMath0923.11152OpenAlexW1970772895MaRDI QIDQ1284240

Daniel R. Replogle

Publication date: 15 August 1999

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jabr.1998.7652

zbMATH Keywords

Kummer extensionsSwan modulesintegral normal bases

Mathematics Subject Classification ID

Separable extensions, Galois theory (12F10) Class numbers, class groups, discriminants (11R29)

Related Items (5)

Kernel groups and nontrivial Galois module structure of imaginary quadratic fields ⋮ Nontrivial Galois module structure of cyclotomic fields ⋮ Swan modules and Hilbert-Speiser number fields ⋮ Cyclotomic Swan subgroups and irregular indices ⋮ On a normal integral basis problem over cyclotomic \(Z_{p}\)-extensions. II.

Cites Work

• Nontrivial lower bounds for class groups of integral group rings
• Relative Galois module structure of quadratic extensions
• Normal integral bases in Kummer extensions of prime degree
• A Mayer-Vietoris sequence for class groups
• Swan modules and Hilbert-Speiser number fields
• Galois module structure of abelian extensions.
• Arithmetic and Galois module structure for tame extensions.
• Class Groups of Integral Group Rings
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