Radical of Primary Ideal is Smallest Prime Ideal

Theorem
Let $R$ be a commutative ring.

Let $\mathfrak q$ be a primary ideal of $R$.

Let $\map \Rad {\mathfrak q}$ be the radical of $\mathfrak q$.

Then $\map \Rad {\mathfrak q}$ is the smallest prime ideal including $\mathfrak q$.