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.

1. S. Abhyankar, On the ramification of algebraic functions, Amer. J. Math. vol. 77 (1955) pp. 575-592. 2. C. Chevalley, On the theory of local rings, Ann. of Math. vol. 44 (1943), pp. 680-708. 3. -, Introduction to the theory of algebraic functions of one variable, New York, 1951. 4. S. MacLane and O. F. G. Schilling, Zero-dimensional branches of rank one on algebraic varieties, Ann. of Math. ...