Automorphisms of subrings of \(\text{RFM}(R)\)
type: Item
instance of: scholarly article
title: Automorphisms of subrings of \(\text{RFM}(R)\)
zbMATH Open document ID: 0815.16012
DOI: 10.1007/BF01198666
author: José Luis García
author: Juan Jacobo Simón
published in: Archiv der Mathematik
publication date: 1995-04-18T00:00:00Z
review text: Let \(R\) be an associative ring with identity element. \(\text{RFM}(R)\) denotes the ring of row-finite matrices over \(R\) and \(FC(R)\) its twosided ideal consisting of all the matrices with a finite number of nonzero columns. In this paper, we consider subrings \(\Sigma\) of \(\text{RFM}(R)\) such that \(FC(R) \subseteq \Sigma\), and study some properties of the automorphisms \(\sigma\) of such subrings. Most of these properties are related to the structure of the endomorphism ring of the left \(R\)-module \(R^{(\mathbb{N})} \sigma(e)\), where \(e\) is the matrix with 1 in the left upper corner, 0 elsewhere. In particular, it is shown that this endomorphism ring is not necessarily isomorphic to the ring \(R\).
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 16W20
zbMATH DE Number: 743513
zbMATH Keywords: ring of row-finite matrices
zbMATH Keywords: automorphisms
zbMATH Keywords: endomorphism ring
reviewed by: Juan L. G. Guirao
MaRDI profile type: Publication
cites work: Infinite matrix types which determine Morita equivalence
cites work: On dense subrings of RFM(R)
cites work: Q4056148
cites work: Morita Equivalence and Infinite Matrix Rings
cites work: Q5673086
cites work: Endomorphism rings of infinitely generated projective modules
full work available at URL: https://doi.org/10.1007/bf01198666
OpenAlex ID: W2356127786
description: scientific article; zbMATH DE number 743513