On a power integral bases problem over cyclotomic \(\mathbb{Z}_p\)-extensions

DOI10.1006/jabr.2000.8454zbMath0990.11060OpenAlexW2087004065MaRDI QIDQ1841818

Humio Ichimura

Publication date: 3 May 2001

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

Full work available at URL: https://doi.org/10.1006/jabr.2000.8454

zbMATH Keywords

Iwasawa theorypower integral basis

Mathematics Subject Classification ID

Iwasawa theory (11R23) Algebraic numbers; rings of algebraic integers (11R04)

Related Items (5)

Indices of Kummer extensions of prime degree ⋮ Biographical Sketch of Professor Humio Ichimura ⋮ On a quotient of the unramified Iwasawa module over an abelian number field ⋮ A note on integral bases of unramified cyclic extensions of prime degree ⋮ On a normal integral basis problem over cyclotomic \(Z_{p}\)-extensions. II.

Cites Work

• The Iwasawa invariant \(\mu_p\) vanishes for abelian number fields
• Unités cyclotomiques, unités semilocales et \(\mathbb{Z}_\ell\)-extensions. II
• Initial layers of \(\mathbb{Z}_p\)-extensions and Greenberg's conjecture
• On a relative normal integral basis problem over abelian number fields
• On a normal integral bases problem over cyclotomic \(\mathbb{Z}_p\)-extensions
• On the Iwasawa invariants of certain real abelian fields
• On power integral bases of unramified cyclic extensions of prime degree
• On \(\mathbb Z_{\ell}\)-extensions of algebraic number fields
• ON THE IWASAWA INVARIANTS OF CERTAIN REAL ABELIAN FIELDS II
• On the Iwasawa Invariants of Totally Real Number Fields
• The Group of Unramified Kummer Extensions of Prime Degree
• On p-adic L-functions and normal bases of rings of integers.
• On the units of algebraic number fields

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