Especially to Neil: T.Y. Lam has confirmed that the ring Z[[x]] of formal power series in one variable over the integers is a unique factorization domain. I was told this is based on this paper by Pierre Samuel: On unique factorization domains. Illinois J. Math. 5 1961 1--17. MR 22#12121 George Bergman mentioned that there is also another paper by Samuel about UFD's in the Monthly: 75(1968)945-952, "which apparently includes discussion of power series". --Dan