Some characterizations of quasi-Frobenius rings

Abstract

A ring R is called right WP-injective if for any \(0\ne a\in R\), there exist \(b\in R\) such that \(ab=ba\ne 0\) and any right R-homomorphism from abR to R extends to an endomorphism of R. A series of conditions under which right WP-injective rings are quasi-Frobenius rings are given, some results improve known results on quasi-Frobenius rings.