Hartshorne gives a correspondence between Cartier divisors of X and Weil Divisors of X, when X is integral separated locally factorial noetherian scheme.
I understand given a Cartier Divisor how to define a Weil Divisor. But I don't understand the the other way correspondence.
I have seen a proof of how a Weil Divisor D induces a Weil Divisor $D_x$ om the local scheme Spec$\mathcal O_x$ in Restricting a Weil divisor to a local scheme. And $D_x$ is a principal divisor. But I don't understand after that.
Can someone please help Thanks in advance.