Morita-like equivalence of infinite matrix subrings
type: Item
instance of: scholarly article
title: Morita-like equivalence of infinite matrix subrings
zbMATH Open document ID: 0816.16007
author: R. F. Turner-Smith
author: Xu Yonghua
author: K. P. Shum
published in: Journal of Algebra
publication date: 1995-07-17T00:00:00Z
review text: Let \(\Gamma\) be an arbitrary index set, \(R\) a ring with 1. If \(T\) is the ring of row-finite \(\Gamma \times \Gamma\) matrices over \(R\) which have only finitely many non-zero columns, and \(\ell^ 2 = \ell \in T\) satisfies \(T\ell T = T\), then the categories of unitary right modules over \(T\) and \(S = \ell T\ell\), respectively, are equivalent in view of Theorem 3.2, the main result of the paper. Here a right \(T\)-module \(M\) is called unitary if \(MT = M\) holds.
Mathematics Subject Classification ID: 16D90
Mathematics Subject Classification ID: 16S50
zbMATH DE Number: 571355
zbMATH Keywords: Morita equivalence
zbMATH Keywords: ring of row-finite matrices
zbMATH Keywords: categories of unitary right modules
reviewed by: Ánh Pham Ngoc
MaRDI profile type: Publication
full work available at URL: jabr.1993.1166
OpenAlex ID: W2020923863
DOI: 10.1006/JABR.1993.1166
description: scientific article; zbMATH DE number 571355