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

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Robin Chapman

Posts: 281
Registered: 5/29/08
Re: trace map is surjective
Posted: Jan 24, 2013 8:35 AM
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On 24/01/2013 12:53, 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?


For instance

www.math.uconn.edu/~kconrad/blurbs/galoistheory/separable2.pdf

Of course in this context it is easy. The minimum polynomial
of any element in the extension but not in the ground
field is x^2 - a x + b and a is nonzero lest the extension
be separable. Of course, a is a trace.



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