> 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/ eircom.net tel: +353-86-2336090, +353-1-2842366 s-mail: School of Mathematics, Trinity College Dublin