Abstract

In this paper the authors show that if \(R\) is a prime ring and \(e\) is an idempotent in \(R\), then \(eR_R\) is nonsingular, CS and \(1<\text{u-}\dim(eR_R)<\infty\) if and only if \(_ReR\) is nonsingular, CS and \(1<\text{u-}\dim(_ReR)<\infty\). Examples are provided to show that the finiteness of the uniform dimension is also in this case necessary.