[FOM] UFD example?

[joeshipman@aol.com]

What is an example of Unique Factorization Domain which is neither a 
Principal Ideal Domain nor (isomorphic to) a polynomial ring? (By a 
polynomial ring I mean a ring R[x] formed by adjoining an indeterminate 
to a ring; such rings are UFDs if the original ring was, by the 
generalized Gauss Lemma).

My earlier query about rings with a transfinite Euclidean algorithm is 
separate from this, because such rings are PIDs (by the usual proof, 
using the algorithm to find a "GCD" of two elements in the ideal they 
generate).

-- JS


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