Let $A$ be a Noetherian [integral domain](/page/Integral%20Domain), and let $f\in A$ be a nonzero nonunit. If $\mathfrak p\trianglelefteq A$ is a prime ideal minimal among the prime ideals containing the principal ideal $(f)$, then
Consequently, let $k$ be an [algebraically closed field](/page/Algebraically%20Closed%20Field), let $X$ be an irreducible affine variety over $k$, and let $f\in k[X]$ be a nonzero nonunit. Then every irreducible component of the closed subset