Approximating rings with local units via automorphisms
type: Item
instance of: scholarly article
title: Approximating rings with local units via automorphisms
zbMATH Open document ID: 0930.16021
DOI: 10.1023/A:1026460815618
author: Jeremy Haefner
author: Gene Abrams
author: Ángel del Río
published in: Acta Mathematica Hungarica
publication date: 1999-10-31T00:00:00Z
review text: Let \(A\) be a ring with local units. An approximation of \(A\) is an overring \(T\) containing \(A\) such that \(A=ATA\) and for each \(0\neq t\in T\) there exist \(a\), \(b\) with \(atb\neq 0\). There are three classical unital approximations of \(A\), namely, the Dorroh extension \(C(A)\), the endomorphism ring \(E(A)=\text{End}(_AA)\), and the translation hull \(Q(A)\). If \(T\) is a unital approximation of \(A\), then the restriction induces a homomorphism between the automorphism groups \(\Aut(T)\) and \(\Aut(A)\). The aim of the paper is a comparison of these automorphism groups by using the canonical restriction homomorphism.
Mathematics Subject Classification ID: 16U60
Mathematics Subject Classification ID: 16W20
Mathematics Subject Classification ID: 16S50
zbMATH DE Number: 1355012
zbMATH Keywords: automorphism groups
zbMATH Keywords: endomorphism rings
zbMATH Keywords: incidence rings
zbMATH Keywords: rings with local units
zbMATH Keywords: approximations of rings
zbMATH Keywords: Dorroh extensions
zbMATH Keywords: translational hulls
MaRDI profile type: Publication
full work available at URL: a:1026460815618
OpenAlex ID: W1782853211
description: scientific article; zbMATH DE number 1355012