4.4 Module intersection 2

Let R be an affine ring, and let $I,J,K\subseteq R$ be ideals. One can compute generators for the intersection $L=I\cap J\cap K$ in the follwing way: L is the kernel of the R-module homomorphism $\phi:R\rightarrow R/I\oplus R/J \oplus R/K$ which sends 1 to (1,1,1).

Lemma 4..7  

$$I\cap J\cap K=modulo( \left( \begin{array}{c} 1\\ 1\\ 1\\ ... ...I & 0 & 0 \\ 0 & J & 0 \\ 0 & 0 & K \\ \end{array}\right) ).$$