I'm currently preparing for a talk about the algebraic study of D-Modules. For some propositions I need to give a quick excursion to commutative algebra - a field I'm not familiar with at all. I just recently learned what an Annihilator is and the professor who is hosting the talk scribbled a note on my paper below the definition of it:
"In commutative algebra we can write the radical ideal of an ideal I as: $$\sqrt{I}=y_1 \cap y_2 \cap ... \cap y_n$$ We call $y_i$ assoiated to I."
And I'm completely confused what he meant by that. I gather it has something to do with the Lasker-Noether-Theorem, which states that we can find $y_i$ that are primary, but can we say even more about them if we're only looking at the radical ideal? $y_i$ need to be prime ideals to somewhat make sense to the definition of the support of a module I read in our script, but I don't see why they'd need to be?