When cyclic singular modules over a simple ring are injective (Q1812160)

Let \(R\) be a simple ring. It is shown that \(R\) is Morita equivalent to a right PCI (proper cyclics are injective) domain if and only if every singular cyclic right \(R\)-module is quasi-continuous, and furthermore if every proper cyclic right \(R\)-module is quasi-continuous then the right uniform dimension of \(R\) is at most 2.