(1) "For affine variety $V$ of $\mathbb{A}^{n}$ such that its coordinate ring is UFD, closed subvariety of $V$ which has codimension 1 is cut out by a single equation."
I looked at the proof of this statement, Where I have been using UFD in I do not know...
(2) I want to see proof of follwing statement....
"Any closed subvariety of affine normal variety with codimension 1 is cut out by a single equation."