On von Neumann regular rings. X
type: Item
instance of: scholarly article
title: On von Neumann regular rings. X
zbMATH Open document ID: 0544.16006
author: Roger Yue Chi Ming
published in: Collectanea Mathematica
publication date: 1983-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/44374
review text: [Part IX, cf. the article reviewed above.] In the first part of the paper, rings having a regular classical left quotient ring Q are considered and conditions for Q to be continuous, reduced, strongly regular and semi-simple Artinian are studied. In the second part, the following definition is introduced: A left A-module M is called an NCI module if, for any left submodule P containing a non-zero complement left submodule of M and any left submodule N of M which is isomorphic to P, every left A-homomorphism of N into P extends to an endomorphism of M. Injective modules are NCI and NCI-modules are continuous. The author connects this definition with various other notions, such as regular, strongly regular, quasi-Frobenius and semi- simple Artinian rings (e.g. A is semi-simple Artinian iff every finitely generated left module is NCI).
Mathematics Subject Classification ID: 16E50
Mathematics Subject Classification ID: 16D50
Mathematics Subject Classification ID: 16Kxx
zbMATH DE Number: 3865506
zbMATH Keywords: generalization of injectivity
zbMATH Keywords: regular classical left quotient ring
zbMATH Keywords: NCI- modules
zbMATH Keywords: strongly regular
zbMATH Keywords: quasi-Frobenius
zbMATH Keywords: semi-simple Artinian rings
zbMATH Keywords: finitely generated left module
reviewed by: Hans H. Storrer
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3865506