A UFD for which the related formal power series ring is not a UFD

Asked Sep 02 '15 at 15:11

Active Sep 10 '15 at 21:37

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I know that the proposition $$ A \text{ is a UFD } \Rightarrow A[[X]] \text{ is a UFD }$$ is false.

Wikipedia states that if $B=K[x,y,z]/(x^2+y^3+z^7)$ then $A=B_{(x,y,z)}$ is a counterexample, but I can't show that $A$ is a UFD and $A[[X]]$ isn't.

Are there other known counterexample?

edited Sep 10 '15 at 21:37

user26857

asked Sep 02 '15 at 15:11

karmalu

3

There is a counterexample by Samuel, with $A$ being of characteristic $2$, see here , reference [7]. – Dietrich Burde Sep 02 '15 at 15:21

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