Let K be any field which may not be algebraically closed, V a finite-dimensional Ž . vector space over K, g GL V where the order of can be finite or infinite.Ž . ² : Ž Ž .. ² : THEOREM. If dim V F 3, then both K V and K ‫ސ‬ V are rational K Ž . s purely transcendental over K. Similar results hold for a cyclic affine action.

No abstract

Let κ be a field of characteristic 2. The author's previous results (Arch. Math. (1994)) are used to prove the excellence of quadratic extensions of κ. This in turn is used to determine the Witt kernel of a quadratic extension up to Witt equivalence. An example is given to show that Witt equivalence cannot be strengthened to isometry.

For a field k of characteristic not two, it is known that k is algebraically closed in the function field of any (non-degenerate) quadratic form in three or more variables. In this note we consider fields of characteristic two and decide when Jf e is algebraically closed in a function field of a quadratic fc-form. For quadratic forms in three variables this has recently been done by Ohm.

No abstract