Integrally closed rings which are Prufer

Let R be a commutative ring with zero divisors. It is well known that if R is integrally closed, then R is a Prufer domain if and only if there is an integer n > 1 such that, for all . We soften this result for commutative rings with zero divisors by proving that this integer n does not have to work for all a, b is an element of R.