This note is devoted to proving
the theorem that every right quasi-projective module over a semi-primary ring R has
the double centralizer property if and only if R is a direct sum of primary rings, and
to discussing some of its consequences. In particular, this theorem places a strong
necessary condition on a large class of the balanced rings of Camillo which are both a
specialization of Thrall’s QF − l rings and a generalization of the uniserial rings of
Köthe.