The dual of a theorem of Goldman
Goldman showed that a preradical \(\sigma\) on the category of modules over a ring R is a left exact radical if and only if there exists an injective module E such that \(\sigma (M)=\cap \{\ker \alpha |\) \(\alpha \in \hom _ R(M,E)\}\). If \(\sigma\) (R) has a projective cover, it is shown that \(\sigma\) is idempotent and preserves epimorphisms if and only if there exists a projective module P such that \(\sigma (M)=\sum \{im \alpha |\) \(\alpha \in \hom _ R(P,M)\}\).
scientific article; zbMATH DE number 4004405