When is the radical associated with a module a torsion?

Abstract

For an arbitrary R-module M we consider the radical (in the sense of Maranda)G M, namely, the largest radical among all radicalsG, such thatG(M). We determine necessary and sufficient on M in order for the radicalG(M) to be a torsion. In particular,G(M) is a torsion if and only if M is a pseudo-injective module.