Normal integral bases in Kummer extensions of prime degree

DOI10.5802/jtnb.107zbMath0822.11076OpenAlexW1982746867MaRDI QIDQ1340678

Eugenio Jesús Gómez Ayala

Publication date: 26 January 1995

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_1994__6_1_95_0

zbMATH Keywords

free modulenormal integral basisGalois module structurering of integerstamely ramified Kummer extension

Mathematics Subject Classification ID

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

Related Items (max. 100)

On the ring of \(p\)-integers of a cyclic \(p\)-extension over a number field ⋮ Indices of Kummer extensions of prime degree ⋮ Normal integral bases for cyclic Kummer extensions ⋮ On normal integral bases of unramified abelian \(p\)-extensions over a global function field of characteristic \(p\) ⋮ Normal bases for quadratic extensions inside cyclotomic fields ⋮ On the ring of integers of a tame Kummer extension over a number field. ⋮ Note on the ring of integers of a Kummer extension of prime degree. II ⋮ On a theorem of Kawamoto on normal bases of rings of integers ⋮ Note on Galois descent of a normal integral basis of acyclic extension of degree \(p\) ⋮ Note on the ring of integers of a Kummer extension of prime degree. IV ⋮ Note on the ring of integers of a Kummer extension of prime degree. III ⋮ Hilbert-Speiser number fields and Stickelberger ideals ⋮ Hopf-Galois module structure of tamely ramified radical extensions of prime degree ⋮ Swan modules and realisable classes for Kummer extensions of prime degree ⋮ Note on the ring of integers of a Kummer extension of prime degree. V. ⋮ On a normal integral basis problem over cyclotomic \(Z_{p}\)-extensions. II.

Cites Work

• On normal integral bases
• Remark on On normal integral bases
• Elliptic functions and rings or integers
• On Fröhlich's conjecture for rings of integers of tame extensions
• A remark about the Galois module structure in ray class fields over imaginary quadratic number fields
• On Integral Bases
• The module structure of Kummer extensions over Dedekind domains.
• Arithmetic and Galois module structure for tame extensions.
• Galois Module Structure of Rings of Integers in Kummer Extensions
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