The Artin-Hasse power series and p-adic group rings
type: Item
instance of: scholarly article
title: The Artin-Hasse power series and p-adic group rings
zbMATH Open document ID: 0731.20006
DOI: 10.1016/0022-314X(91)90039-E
author: Klaus Hoechsmann
author: Jürgen Ritter
published in: Journal of Number Theory
publication date: 1991-01-01T00:00:00Z
review text: Let p be an odd prime and \({\mathcal A}\) a finite abelian \(p\)-group. Let \({\mathbb{Z}}_{p}{\mathcal A}\) be the \(p\)-adic group ring of \({\mathcal A}\) and \({\mathcal E}({\mathcal T})\) the well known \(p\)-adically integral power series exp(\(\sum^{\infty}_{n=0}p^{-n}{\mathcal T}^{p^{n}})\). It is shown that the multiplicative group of \({\mathbb{Z}}_{p}{\mathcal A}\) formed by \(\{1+\sum_{z\in {\mathcal A}}a_{z}(z-2+z^{-1})|\) \(a_{z}\in {\mathbb{Z}}_{p}\}\) has the \({\mathbb{Z}}_{p}\)-basis \(\{\) \({\mathcal E}(z-2+z^{- 1}|\) \(1\neq z\in {\mathcal A}\}\).
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 20C11
Mathematics Subject Classification ID: 16U60
Mathematics Subject Classification ID: 16S34
zbMATH DE Number: 4208359
zbMATH Keywords: finite abelian \(p\)-group
zbMATH Keywords: \(p\)-adic group ring
zbMATH Keywords: multiplicative group
reviewed by: Todor Mollov
MaRDI profile type: Publication
cites work: Q5792522
cites work: Généralisation d'un Lemme de Kummer
cites work: Local units and circular index in abelian \(p\)-group rings
cites work: Logarithms and units in p-adic Abelian group rings
cites work: Q4198893
full work available at URL: 0022-314x(91)90039-e
OpenAlex ID: W2071256659
description: scientific article; zbMATH DE number 4208359