# the topology of power series ring

Hi, everyone.

Let $A$ be a complete DVR with uniformizer $t$, $R:=A[[X]]$. What is the natural topology of $R$ ?

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The ring $R$ is complete both for the $\langle X \rangle$-adic topology and for the $\langle t, X \rangle$-adic topology. So it depends on what you want to study about $R$. –  Leo Alonso Apr 29 '13 at 14:20
I'm sure an answer can be very quickly found at math.stackexchange.com –  Olivier Apr 29 '13 at 14:21
The question is subtler than it appears, depending on the topology you choose its formal spectrum is completely different. –  Leo Alonso Apr 29 '13 at 14:27
I think there is no "natural" topology, as Leo says. –  Filippo Alberto Edoardo Apr 29 '13 at 15:39
discrete valuation ring I suppose, en.wikipedia.org/wiki/Discrete_valuation_ring –  Pietro Majer Apr 29 '13 at 19:52