Dinesh Khurana

Abstract
Several equivalent formulations of the question of the title are given. In particular, it is proved that a right perfect right self-injective ring R is right PF if and only if R/Z(_RR) is a semiprime ring. It is shown that a right  perfect left quasi-continuous ring is left and right Kasch. Some necessary and sufficient conditions for a semiperfect ring to be right Kasch are given.