Perfect rings for which the converse of Schur's lemma holds

If $M$ is a simple module over a ring $R$ then, by the Schur's lemma, the endomorphism ring of $M$ is a division ring. However, the converse of this result does not hold in general, even when $R$ is artinian. In this short note, we consider perfect rings for which the converse assertion is true, and we show that these rings are exactly the primary decomposable ones.