If $I$ and $J$ are two coprime ideals in a unitary commutative ring $R$, i.e. $I+J=R$, then $IJ=I\cap J$.
The above fact has been stated without proof in almost every textbook I have referred. No one seems to be giving any direction for proof.
I know that one direction of the proof ( $IJ\subseteq I\cap J$ ) is trivial.
How do I go about the other direction?