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

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Timothy Murphy

Posts: 657
Registered: 12/18/07
Re: trace map is surjective
Posted: Jan 24, 2013 8:20 AM
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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.)

Timothy Murphy
e-mail: gayleard /at/
tel: +353-86-2336090, +353-1-2842366
s-mail: School of Mathematics, Trinity College Dublin

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