Quasi regular modules and endomorphism ring of regular modules (Q1073155)

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.