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In this paper, we will prove that any $\A^3$-form over a field $k$ ofcharacteristic zero is trivial provided it has a locally nilpotent derivationsatisfying certain properties. We will also show that the result of T.Kambayashi on the triviality of separable $\A^2$-forms over a field $k$ extendsto $\A^2$-forms over any one-dimensional Noetherian domain containing $\bQ$.

On Separable $\A^2$ and $\A^3$-forms