``Galois module structure of quaternion extensions of degree 8

DOI10.1006/jabr.1998.7674zbMath0989.11060OpenAlexW1982326408MaRDI QIDQ1282347

Bouchaïb Sodaïgui

Publication date: 17 June 1999

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

Full work available at URL: https://doi.org/10.1006/jabr.1998.7674

zbMATH Keywords

Stickelberger elementsSteinitz classesquaternion extensions

Mathematics Subject Classification ID

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

Related Items

Relative Galois module structure of octahedral extensions ⋮ On Steinitz classes, realizable Galois module classes and embedding problems for non-abelian extensions of degree a power of 2 ⋮ Realizable classes of nonabelian extensions of order \(p^3\) ⋮ Realizable Galois module classes over the group ring for non abelian extensions ⋮ Relative Galois module structure and Steinitz classes of dihedral extensions of degree 8 ⋮ Realizable classes of quaternion extensions of degree \(4\ell\) ⋮ On realizable Galois module classes by the inverse different ⋮ On realizable Galois module classes and Steinitz classes of nonabelian extensions ⋮ Galois module structure for dihedral extensions of degree 8: realizable classes over the group ring ⋮ CLASSES DE STEINITZ D'EXTENSIONS NON ABÉLIENNES À GROUPE DE GALOIS D'ORDRE 16 OU EXTRASPÉCIAL D'ORDRE 32 ET PROBLÈME DE PLONGEMENT

Cites Work

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• Relative Galois structure of rings of integers.
• Steinitz classes of relative Galois extensions of 2-power degree and embedding problems
• Realizable classes by non-abelian metacyclic extensions and Stickelberger elements
• Galois module structure of abelian extensions.
• Arithmetic and Galois module structure for tame extensions.