In occassions where I need to find the minimal primes associated to an ideal / find a primary decomp., sometimes I can do it just fine, sometimes I find myself completely blind in the search for it.
So Im here asking for general heuristics for this, and also for relevant lemmas and theorems that are frequently used in such situations.
As an example, could someone please explain to me how to find:
- the minimal primes
- a primary decomposition
Of an ideal such as: $J = ( XZ-Y^2 , X^3-YZ)$ , to be understood inside the polynomial ring in the variables X Y Z over a field k.
PS: I already looked for some similar questions on this site, but the ones I found were not very clarifying.