A module M is said to be coretractable if there exists a nonzero homomorphism of every nonzero factor of M into M. We prove that all right (left) modules over a ring are coretractable if and only if the ring is Morita equivalent to a finite product of local right and left perfect rings.
A module M is said to be coretractable if there exists a nonzero homomorphism of every nonzero factor of M into M. We prove that all right (left) modules over a ring are coretractable if and only if the ring is Morita equivalent to a finite product of local right and left perfect rings. (en)