# Thread: Intersection of Ideals

1. ## Intersection of Ideals

True or False:

If $R$ is a noetherian ring and if $A$ and $B$ are subsets of $R$, then the intersection $\cap$, of the ideals they generate is generated by a finite subset of $A\cap B$

A hint would preferred to the full solution, I just don't know how to start this, thanks.

2. Hi

Perhaps look in $k[x,y]$ for (nice) subsets $A,B$ such that $\cap\neq 0$ and $A\cap B=\emptyset$