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Timeline for Is it true that, as $\Bbb Z$-modules, the polynomial ring and the power series ring over integers are dual to each other?

Current License: CC BY-SA 2.5

19 events
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Jul 19, 2021 at 16:48 comment added Michael "Now choose any old integers" \to "Now choose any odd integers" :-)
Dec 31, 2009 at 12:35 vote accept Maharana
Dec 31, 2009 at 11:52 comment added Kevin Buzzard OK, fixed. Thanks Qiaochu for pointing that out!
Dec 31, 2009 at 11:26 history edited Kevin Buzzard CC BY-SA 2.5
clarification; Post Made Community Wiki
Dec 31, 2009 at 10:54 history edited Kevin Buzzard CC BY-SA 2.5
typos/clarifications
Dec 31, 2009 at 10:36 history edited Kevin Buzzard CC BY-SA 2.5
typo
Dec 31, 2009 at 10:18 history edited Kevin Buzzard CC BY-SA 2.5
typo
Dec 31, 2009 at 10:13 history undeleted Kevin Buzzard
Dec 31, 2009 at 10:13 history edited Kevin Buzzard CC BY-SA 2.5
typo
Dec 31, 2009 at 9:54 history deleted Kevin Buzzard
Dec 31, 2009 at 9:53 history edited Kevin Buzzard CC BY-SA 2.5
deleted entire answer. I can't remove the post though because the answer has been accepted :-(
Dec 31, 2009 at 9:47 history edited Kevin Buzzard CC BY-SA 2.5
added serious edit: answer as it stands is false.
Dec 31, 2009 at 9:39 comment added Qiaochu Yuan You don't seem to have excluded the possibility that f(e_n) = 0 for all n but f is not the zero homomorphism; in other words, you don't seem to have shown that there are no nontrivial homomorphisms (prod Z)/(sum Z) -> Z.
Dec 31, 2009 at 9:39 vote accept Maharana
Dec 31, 2009 at 9:52
Dec 31, 2009 at 8:58 comment added Kevin Buzzard Because if all the c_i are 1 then sum_i 2^ic_i=-1 in Z_2, so f(1,2,4,8,...)=-1 would not be a contradiction.
Dec 31, 2009 at 8:51 comment added Qiaochu Yuan Not that I'm not convinced, but why is the step where you pick d_i necessary?
Dec 31, 2009 at 8:43 comment added Kevin Buzzard NB to justify the "old chestnut" tag: if I remember correctly this proof (or some variant of it, possibly not mentioning p-adic numbers but morally doing the same thing) is in Kaplansky's "infinite abelian groups", so dates back to at least the 60s. Imre Leader told me this question when I was an undergrad.
Dec 31, 2009 at 8:37 history edited Kevin Buzzard CC BY-SA 2.5
clarification
Dec 31, 2009 at 8:29 history answered Kevin Buzzard CC BY-SA 2.5
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