Let $R$ be a commutative ring with unity. Let $I$ be an ideal of $R.$ Then I know that $$\operatorname {rad} ({I}) = \bigcap\limits_{\substack {p \supseteq I \\ \text {p prime}}} p.$$ Now let $I = (0).$ Then by the similar reasoning $$\operatorname {rad} ({0}) = \bigcap\limits_{\text {p prime}} ...