A property of weakly Krull domains

We show that a weakly Krull domain D satisfies (*): for every pair a, b is an element of D\{0} there is an n = n(a; b) is an element of N such that (a; b(n)) is t-invertible. For D Noetherian, D satisfies (*) if and only if every grade-one prime ideal of D is of height one. We also show that a modification of (*) can be used to characterize Noetherian domains that are one-dimensional.