Isomorphisms of certain locally nilpotent finitary groups and associated rings.
type: Item
instance of: scholarly article
title: Isomorphisms of certain locally nilpotent finitary groups and associated rings.
zbMATH Open document ID: 1055.16021
DOI: 10.1023/B:ACAP.0000027533.59937.14
author: Feride Kuzucuoglu
author: Vladimir M. Levchuk
published in: Acta Applicandae Mathematicae
publication date: 2004-08-20T00:00:00Z
review text: Let \(K\) be a ring, \(X\) a totally ordered set and \(V\) a free \(K\)-module on the set \(X\). Endomorphisms of \(V\) can be described by row-finite matrices over \(K\) with rows and columns indexed by the ordered set \(X\). Let \(N(X,K)\) be the ring of all such matrices with zeros on and above the main diagonal and with non-zeros in only finitely many positions below. If either \(X\) is finite or \(K\) has no zero-divisors the authors describe the isomorphisms between \(N(X,K)\) and \(N(X',K')\) for \(X'\) a (possibly) second ordered set and \(K'\) a second ring. Their adjoint groups and associated Lie rings are also described.
Mathematics Subject Classification ID: 16N40
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 16W20
Mathematics Subject Classification ID: 16W10
Mathematics Subject Classification ID: 20H25
zbMATH DE Number: 2093676
zbMATH Keywords: chains
zbMATH Keywords: finitary matrix rings
zbMATH Keywords: radical rings
zbMATH Keywords: adjoint groups
zbMATH Keywords: associated Lie rings
zbMATH Keywords: standard isomorphisms
zbMATH Keywords: locally nilpotent rings
reviewed by: B. A. F. Wehrfritz
MaRDI profile type: Publication
full work available at URL: b:acap.0000027533.59937.14
OpenAlex ID: W2162725835
description: scientific article; zbMATH DE number 2093676