I was trying to prove a theorem in algebraic geometry which basically held if and only if this lemma held. Here’s the lemma:

**Lemma: **Given any ring $A$, a prime ideal $ \mathfrak{p} \subset A$, and a finite collection of ideals $I_j,$ where $j \in \{1, 2, … , n\}$, then if $I$ is the intersection of the ideals, then $I \subset \mathfrak{p}$ implies that $I_j \subset \mathfrak{p}$ for some $j \in \{1, 2, … , n\}$. Continue reading “A Pretty Lemma About Prime Ideals and Products of Ideals” »