Is there a ring R with infinite elements with $\mathrm{char}(R)$ not $0$?

Question

True or false?

"Every ring R with infinite elements has $\mathrm{char}(R)=0$"

My answer was that $\Bbb Z_2 [x] $ is a ring with infinite elements such that for a polynomial $f(x) $ in $\Bbb Z_2 [x] $, the sum of $f(x)+f(x)=0$, in particular, for the unit element, $1+1=0$, so $\mathrm{char}(\Bbb Z_2 [x]) =2$ and the statement is False.

Is this correct?

That question and solution are easily found on the site, namely here and here. You really ought to search and find those before asking. — rschwieb, Sep 10 '17 at 11:54
Dear @bof : What is the difference, in your mind, between proof-verification and seeing ones own answer confirmed in several other places as proof? (Don't worry, I plan to ignore the condescension of your comment as well-intended.). Regards — rschwieb, Sep 10 '17 at 20:27
@bof If the thing being verified wasn't present in other solutions, I would not be speaking so, of course. — rschwieb, Sep 10 '17 at 20:29

score 2 · Accepted Answer · answered Sep 10 '17 at 11:34

2

Yes, that is correct.$ $$ $$ $$ $

answered Sep 10 '17 at 11:34

Kenny Lau

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This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post. - From Review – José Carlos Santos Sep 10 '17 at 12:02
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@JoséCarlosSantos "Yes" is definitely an answer to "is this correct". – Kenny Lau Sep 10 '17 at 12:26

Is there a ring R with infinite elements with $\mathrm{char}(R)$ not $0$?

1 Answers1