Quasi regular modules and endomorphism ring of regular modules
type: Item
instance of: scholarly article
title: Quasi regular modules and endomorphism ring of regular modules
zbMATH Open document ID: 0588.16026
author: A. K. Tiwary
author: B. M. Pandeya
author: D. D. S. Regmi
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 1985-01-01T00:00:00Z
review text: In the first part of the paper, the authors list a number of sufficient conditions for a module M to have a (von Neumann) regular endomorphism ring. These conditions deal with regular modules in the sense of \textit{J. Zelmanowitz} [Trans. Am. Math. Soc. 163, 341-355 (1972; Zbl 0227.16022)] and with various other concepts, taken mainly from \textit{Y. Hirano} [Hiroshima Math. J. 11, 125-142 (1981; Zbl 0459.16009)]. The proofs consist of straightforward applications of known results. In the second part, the notion of regularity is generalized: A right module M is called quasi regular (weakly regular) if for all \(m\in M\) there is an \(f\in M^*\) (the dual) and an epimorphism (homomorphism) \(s: M\to M\) such that \(m=s(m)f(m)\). A few properties of these modules are investigated.
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 16E50
Mathematics Subject Classification ID: 16D80
zbMATH DE Number: 3944077
zbMATH Keywords: regular endomorphism ring
zbMATH Keywords: regular modules
zbMATH Keywords: quasi regular
zbMATH Keywords: weakly regular
reviewed by: Hans H. Storrer
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3944077