Abstract
Let K be a field and let A be a central simple algebra over K. Let ? A and ?2, A be respectively the trace form and the second trace form of A. If K has characteristic not two, it is shown in [U] that ?2, A does not give much more information than the usual trace form. If K has characteristic two, the quadratic form ? A has rank zero. In this article, we show that the second trace form of a central simple algebra A of even degree over a field of characteristic two is non-degenerate and we compute its classical invariants.
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