Let $R$ be a commutative integral domain (with 1). I am looking for a general condition under which for all prime ideals $P$, the meet $\bigcap P^n$ of all the powers of $P$ is $0$. This is true for noetherian domains [Zariski \& Samuel, IV, Cor. 1 to Theorem 12] and evidently true of UFDs, even though UFDs needn't be noetherian (e.g. polynomials in infinitely many variables over a field). Does anyone know good general conditions for this?