On \({\mathbb{Z}}_ p\)-extensions of real abelian fields
type: Item
instance of: scholarly article
title: On \({\mathbb{Z}}_ p\)-extensions of real abelian fields
zbMATH Open document ID: 0697.12005
author: Akira Inatomi
published in: Kodai Mathematical Journal
publication date: 1989-01-01T00:00:00Z
review text: The author intends to show that a result on \({\mathbb{Z}}_ p\)-extensions of real quadratic fields obtained by \textit{T. Fukuda} and \textit{K. Komatsu} [J. Number Theory 23, 238-242 (1986; Zbl 0593.12003)] can be extended in a real abelian case. Namely, let k be a finite abelian extension of rationals \({\mathbb{Q}}\) and p be an odd prime number splitting completely in k. Then, any \({\mathbb{Z}}_ p\)-extension K/k is cyclotomic. The author gives a sufficient condition for the Iwasawa invariant \(\lambda_ p(k)\) of k to vanish under the assumption \((h_ k,p)=1\) for the class number \(h_ k\) of k.
reviewed by: Hideo Yokoi
Mathematics Subject Classification ID: 11R18
Mathematics Subject Classification ID: 11R23
zbMATH DE Number: 4142153
zbMATH Keywords: \(\lambda \) -invariant
zbMATH Keywords: cyclotomic extension
zbMATH Keywords: \({\mathbb{Z}}_ p\)-extensions
zbMATH Keywords: Iwasawa invariant
zbMATH Keywords: class number
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138039105
OpenAlex ID: W2014665393
cites work: On the \(\lambda\) invariants of \(\mathbb Z_p\)-extensions of real quadratic fields
cites work: On the Iwasawa Invariants of Totally Real Number Fields
cites work: On the Class Number of a Relatively Cyclic Number Field
DOI: 10.2996/KMJ/1138039105
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description: scientific article; zbMATH DE number 4142153