I wanted to get an idea on how to find a primary decomposition of an ideal in $\mathbb{Z}[X]$.
I've read a lot of posts, and most of strategies are quite specific for polynomial rings like $K[x,y]$ and the ideals in question are usually generated by monomials. So I was wondering if the strategy involved also works in $\mathbb{Z}[X]$? If not, what are some common techniques that I can try? Say for example
$$I = \langle x^3-2x, x^4-4\rangle$$
Any other examples to illustrate the techniques is also appreciated.
Cheers