TITLE: Seeking Noetherian normal domain with vanishing Picard group but not a UFD
QUESTION [15 upvotes]: Once again, the question says it all.
My motivation is the article on factorization I am writing.  I want to explain (as well as to understand!) why for normal Noetherian domains of dimension greater than one, the obstruction to factoriality is the nonvanishing of the (Weil) divisor class group $\operatorname{Cl}(R)$, not the Picard group $\operatorname{Pic}(R)$ (equivalently, the Cartier divisor class group).
My understanding is that it is equivalent to find a normal Noetherian domain with vanishing Picard group which is not locally factorial.  I would be especially happy to see an example among affine domains, i.e., in which the domain is finitely generated as an algebra over some field.

REPLY [2 votes]: These results hold for any field and for many semigroup rings. The first reference is a paper of mine from 1978 or so in the Canada. Math. J  (I think).
      David F. Anderson