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?

  • 2
    $\begingroup$ There is a counterexample by Samuel, with $A$ being of characteristic $2$, see here , reference [7]. $\endgroup$ Sep 2 '15 at 15:21

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