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Rupert
Posts:
3,797
Registered:
12/6/04
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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:
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> > Does anyone know where I can find a proof that, given a separable
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> > quadratic extension of a field of characteristic two, the trace map is
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> > surjective?
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> I may have misunderstood the question, but isn't
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> tr(ac) = a tr(c)
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> if a is in the ground-field and c in the extension field?
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> So if the trace was not surjective, it would have to be identically zero,
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> which I think it is easy to see is not the case.
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> (Eg if c has minimal equation f(x) = 0 the trace is the x coefficient.)
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Sounds fair enough. Thanks. Being a bit slow today.
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