On the rigidity of small domains
The authors show that a generalization of the conjecture known as Zariski's cancellation problem (let \(V_1\) and \(V_2\) be affine varieties over \(k\) such that \(V_1\times k^n\cong V_2\times k^n\) for some positive integer \(n\). Does it follow that \(V_1\cong V_2?)\) holds for affine curves, using invariant theory on commutative rings. Significant results on this problem were published in 1972 by \textit{S. S. Abhyankar, P. Eakin} and \textit{W. J. Heinzer} [J. Algebra 23, 310--342 (1972; Zbl 0255.13008)].
locally finite iterative higher derivation
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