Normal elements of noncommutative Iwasawa algebras over \(\mathrm{SL}_{3}(\mathbb{Z}_{p})\)
type: Item
instance of: scholarly article
title: Normal elements of noncommutative Iwasawa algebras over \(\mathrm{SL}_{3}(\mathbb{Z}_{p})\)
zbMATH Open document ID: 1448.11195
author: Dong Han
author: Feng Wei
published in: Forum Mathematicum
publication date: 2019-03-20T00:00:00Z
review text: Let \(p\) be a prime integer and let \(\mathbb{Z}_p\) be the ring of \(p\)-adic integers. Using a purely computational approach, the authors proved in the main result of the reviewed paper, namely Theorem 4.1, that each non-zero normal element of a noncommutative Iwasawa algebra over the special linear group \(\mathrm{SL}_3(\mathbb{Z}_p)\) is a unit. This gives a positive answer to an open question in [the second author and \textit{D. Bian}, Int. J. Algebra Comput. 23, No. 1, 215 (2013; Zbl 1267.20009)] and makes up for an earlier mistake in [the second author and \textit{D. Bian}, Int. J. Algebra Comput. 20, No. 8, 1021--1039 (2010; Zbl 1220.20003)] simultaneously. The paper under review is well written and structured with a good organization of the computations.
reviewed by: Peter Danchev
Mathematics Subject Classification ID: 11R23
Mathematics Subject Classification ID: 20C07
Mathematics Subject Classification ID: 16S34
zbMATH DE Number: 7039545
zbMATH Keywords: Iwasawa algebra
zbMATH Keywords: normal element
zbMATH Keywords: \(\mathrm{SL}_{3}(\mathbb{Z}_{p})\)
MaRDI profile type: Publication
full work available at URL: forum-2018-0034
OpenAlex ID: W2787427785
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DOI: 10.1515/FORUM-2018-0034
description: scientific article; zbMATH DE number 7039545