Morita duality for rings with local units
type: Item
instance of: scholarly article
title: Morita duality for rings with local units
zbMATH Open document ID: 0805.16003
published in: Journal of Algebra
publication date: 1995-02-05T00:00:00Z
review text: Using an appropriate generalization of the notion of discrete linearly compact modules over a ring with identity, the authors achieve deeper results about the structure of rings with local units and with Morita duality. The main result translates that of \textit{B. J. Müller} [Math. Z. 119, 63-74 (1971; Zbl 0198.059)] to rings with local units: a ring \(R\) with local units has a Morita duality if and only if \(R\) is discrete linearly compact and injective hulls of simple \(R\)-modules are discrete linearly compact, and an \(R\)-module is reflexive if and only if it is discrete linearly compact. \(R\) has a Morita duality if and only if \(eRe\) has a Morita duality for each \(e^ 2 = e\in R\). If \(R\) is also commutative, then \(R\) has a Morita duality if and only if \(R\) is discrete linearly compact if and only if \(R\) is a (not necessarily finite) direct sum of discrete linearly compact rings with identity.
Mathematics Subject Classification ID: 16D90
Mathematics Subject Classification ID: 16E50
Mathematics Subject Classification ID: 16W80
zbMATH DE Number: 579543
zbMATH Keywords: discrete linearly compact modules
zbMATH Keywords: rings with local units
zbMATH Keywords: Morita duality
zbMATH Keywords: injective hulls of simple \(R\)-modules
zbMATH Keywords: discrete linearly compact rings
author: Ánh Pham Ngoc
author: Claudia Menini
reviewed by: R. Wiegandt
MaRDI profile type: Publication
full work available at URL: jabr.1994.1083
OpenAlex ID: W2027391123
DOI: 10.1006/JABR.1994.1083
description: scientific article; zbMATH DE number 579543