Consider the ring of formal power series $\mathbb{Z}_p[[T]]$ (where $\mathbb{Z}_p$ denotes the ring of $p$-adic integers) with the topology in which a neighborhood basis for $0$ is given by the ideals $I_{n,m} = \left<p^n,T^m\right>$. Is $1+T$ a topological generator for $\mathbb{Z}_p[[T]]$ (i.e., is $\mathbb{Z}_p[[T]]$ the minimal closed subring containing $1+T$)?
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$\begingroup$ Is this a homework? $\endgroup$– Boris BukhCommented Sep 18, 2015 at 18:32
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$\begingroup$ So this site is not for homework questions. You might try posting on math.stackexchange.com, but you would need to explain what you have tried already, rather than just ask for an answer. $\endgroup$– Anthony QuasCommented Sep 18, 2015 at 18:47
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$\begingroup$ math.stackexchange.com/questions/1440622/… $\endgroup$– Will JagyCommented Sep 18, 2015 at 18:53
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1$\begingroup$ This is not a hoework. I was reading about standard Iwasawa algebras and the authors made a claim that trying to understand which I asked this question. And this is my first question on Overflow. I'm sorry I didn't know Overflow was for researchers. Noted. $\endgroup$– Sameer KulkarniCommented Sep 18, 2015 at 19:15
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2$\begingroup$ Possibly helpful question: What topology have you put on this ring? $\endgroup$– S. Carnahan ♦Commented Sep 18, 2015 at 20:01
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