On a generalization of Azumaya's exact rings
type: Item
instance of: scholarly article
title: On a generalization of Azumaya's exact rings
zbMATH Open document ID: 0832.16005
author: Xue Weimin
published in: Journal of Algebra
publication date: 1996-02-20T00:00:00Z
review text: The notion of exact (artinian) rings introduced by Azumaya can be extended in a very natural way to bimodules. Basic properties of exact artinian rings are carried over to the general situation in Sections 1 and 2. The close relations of exact rings with locally distributive rings, duo rings, noetherian rings as well as with Morita (self-) duality are also discussed in this paper. The author proves that linearly compact duo rings are selfdual if the radical is a direct sum of colocal ideals.
Mathematics Subject Classification ID: 16D90
Mathematics Subject Classification ID: 16D20
Mathematics Subject Classification ID: 16P20
zbMATH DE Number: 763907
zbMATH Keywords: exact Artinian rings
zbMATH Keywords: locally distributive rings
zbMATH Keywords: duo rings
zbMATH Keywords: Noetherian rings
zbMATH Keywords: linearly compact duo rings
zbMATH Keywords: radicals
zbMATH Keywords: direct sums
zbMATH Keywords: colocal ideals
reviewed by: Ánh Pham Ngoc
MaRDI profile type: Publication
full work available at URL: jabr.1995.1049
OpenAlex ID: W1964215614
DOI: 10.1006/JABR.1995.1049
description: scientific article; zbMATH DE number 763907