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We recall some basic computations in the Milnor-Witt K-theory of a field,following Morel. We then focus on the Witt K-theory of a field ofcharacteristic two and give an elementary proof of the fact that it isisomorphic as a graded ring to the Rees algebra of the fundamental ideal of theWitt ring of symmetric bilinear forms using Kato's solution to Milnor'sconjecture on quadratic form.

Milnor-Witt K-theory and Witt K-theory of a field