I am Reading Vakil's book "The Rising Sea: Foundations of Algebraic Geometry". After Exercise 5.5.G, he says that we can understand Figure 5.2, which claims:
If X is a locally Noetherian scheme, then a function on X is a zero divisor if it vanishes at some associated points of X.
I don't know how to prove this when X is not affine. Does anyone have a suggestion? Thanks!