Abstract

We prove that for a right perfect ring R, then the following hold: if A, B are projective right R-modules and there exist epimorphisms A→B and B→A, then A is isomorphic to B. A consequence is the following: if A and B are right R-modules with A, an epimorphic image of B and B, an epimorphic image of A, then the projective cover of A and the projective cover of B are isomorphic.