On von Neumann regular rings. XV
type: Item
instance of: scholarly article
title: On von Neumann regular rings. XV
zbMATH Open document ID: 0685.16009
author: Roger Yue Chi Ming
published in: Acta Mathematica Vietnamica
publication date: 1988-01-01T00:00:00Z
review text: [Part XIV cf. An. Univ. Timişoara, Ştiinţe Mat. 25, 75-88 (1987; Zbl 0641.16008).] In the first part of this paper, certain subclasses of regular rings are characterized. Two typical results are: (1) If A is a ring whose essential ideals are two-sided, then A is regular iff A is semi-prime and every simple left module is flat. (2) A is strongly regular iff every simple right module is flat and every complement left ideal is two-sided. The second part is concerned with rings having a classical quotient ring and with divisible modules. Semi-simple Artinian rings, Goldie rings and duo ring also make their appearance.
Mathematics Subject Classification ID: 16E50
Mathematics Subject Classification ID: 16D50
Mathematics Subject Classification ID: 16L60
Mathematics Subject Classification ID: 16D40
zbMATH DE Number: 4122155
zbMATH Keywords: regular rings
zbMATH Keywords: essential ideals
zbMATH Keywords: semi-prime
zbMATH Keywords: strongly regular
zbMATH Keywords: complement left ideal
zbMATH Keywords: classical quotient ring
zbMATH Keywords: divisible modules
zbMATH Keywords: Semi-simple Artinian rings
zbMATH Keywords: Goldie rings
zbMATH Keywords: duo ring
reviewed by: Hans H. Storrer
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4122155