Cogenerator endomorphism rings

Abstract:

If $R$ is a ring and $P$ is a finitely generated projective right $R$-module, what properties of $R$ does the $R$-endomorphism ring of $P$ inherit? Rosenberg and Zelinsky have shown that if $R$ is quasi-Frobenius, and $P$ also has every simple epimorphic image isomorphic to a submodule, then the $R$-endomorphism ring of $P$ is also quasi-Frobenius. In this paper we show that if $R$ is a cogenerator ring, and $P$ is a finitely generated projective right $R$-module with every simple epimorphic image isomorphic to a submodule of $P$, then the $R$-endomorphism ring of $P$ is also a cogenerator ring.