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Nov 22, 2014 at 10:59 comment added Laurent Moret-Bailly All I prove is that if $n\geq2$ then $\dim A\geq2$. If $\dim A\leq1$, this forces property 2.
Nov 22, 2014 at 10:26 comment added user26857 If your claim is true, then the consequence about power series rings seems to have nothing to do with $n=2$. How to reconcile this with the existing counterexamples for $n\ge 3$?
Oct 8, 2014 at 19:30 history answered Laurent Moret-Bailly CC BY-SA 3.0