An associative ring \(R\) with identity is called strongly regular if for each \(a\in R\) there is an \(x\in R\) such that \(a=a^ 2x\). It is easy to see that a Noetherian ring \(R\) is strongly regular if and only if it is a finite direct product of division rings. The author defines an element \(a\) of the ring \(R\) to be prime if the two-sided ideal generated by \(a\) is prime and then shows that \(R\) is Noetherian and strongly regular if and only if (i) \(R\) has no nonzero nilpotent elements, (ii) every element of \(R\) which is not a right unit is a zero-divisor and (iii) the zero element of \(R\) is a finite product of prime elements.