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Topic: trace map is surjective
Replies: 3   Last Post: Jan 24, 2013 8:47 AM

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Rupert

Posts: 3,806
Registered: 12/6/04
Re: trace map is surjective
Posted: Jan 24, 2013 8:47 AM
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On Thursday, January 24, 2013 2:20:15 PM UTC+1, Timothy Murphy wrote:
> Rupert wrote:
>
>
>

> > Does anyone know where I can find a proof that, given a separable
>
> > quadratic extension of a field of characteristic two, the trace map is
>
> > surjective?
>
>
>
> I may have misunderstood the question, but isn't
>
>
>
> tr(ac) = a tr(c)
>
>
>
> if a is in the ground-field and c in the extension field?
>
> So if the trace was not surjective, it would have to be identically zero,
>
> which I think it is easy to see is not the case.
>
> (Eg if c has minimal equation f(x) = 0 the trace is the x coefficient.)
>


Sounds fair enough. Thanks. Being a bit slow today.



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