On regular rings and V-rings

descriptionPublicationkeyboard_double_arrow_right Article 01 Dec 1979 English Publisher:Springer Science and Business Media LLCJournal:Monatshefte f�r Mathematik, volume 88, pages 335-344 (issn: 0026-9255, eissn: 1436-5081,

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Authors: Yue Chi Ming, Roger;

doi: 10.1007/bf01534252

On regular rings and V-rings

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Abstract

In this note, certain generalisations of strongly regular rings are considered in connection with regular rings andV-rings. The result that strongly regular rings are left (and right)V-rings [11] is extended. A condition for prime leftV-rings to be primitive with non-zero socle is given (this is related to a question ofFisher [7, Problem 3]. IfA is an ALD (almost left duo) ring, then (1) a simple leftA-module is injective iff it isp-injective; (2)A is von Neumann regular iff every maximal essential right ideal ofA isf-injective. Characterisations of semi-simple Artinian and simple Artinian rings are given in terms of regular andV-rings.

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University of Paris
France
Université Paris Cité
France

Keywords

cyclic singular left modules, duo rings, V-rings, maximal left subideal, MTE-ring, essential left ideal, Injective modules, self-injective associative rings, von Neumann regular rings and generalizations (associative algebraic aspects), Modules, bimodules and ideals in associative algebras, ALD-ring, von Neumann regular rings

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