A note on von Neumann regular rings
type: Item
instance of: scholarly article
title: A note on von Neumann regular rings
zbMATH Open document ID: 0923.16011
published in: Southeast Asian Bulletin of Mathematics
publication date: 1999-08-25T00:00:00Z
review text: A ring in which all maximal essential left ideals are two-sided ideals (a MELT ring) and over which all singular right modules are flat (a right SF-ring) is shown to be (von Neumann) regular. The proof uses the result that a MERT right SF-ring is regular, obtained by the author and \textit{X. Du} [Commun. Algebra 21, No. 7, 2445-2451 (1993; Zbl 0791.16009)]. As a consequence, a MELT right SF-ring which is injective relative to complemented left ideals is shown to be a self-injective V-ring with bounded index. Finally, an easy example is given of a regular ring with infinite index in which all essential right ideals are two-sided.
reviewed by: Kenneth R. Goodearl
Mathematics Subject Classification ID: 16E50
Mathematics Subject Classification ID: 16D50
zbMATH DE Number: 1267204
zbMATH Keywords: von Neumann regular rings
zbMATH Keywords: right SF-rings
zbMATH Keywords: MELT-rings
zbMATH Keywords: self-injective rings
zbMATH Keywords: essential ideals
author: Jule Zhang
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1267204