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On the rigidity of small domains

Anthony J. Crachiola·Leonid Makar-Limanov
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Abstract

Let $K$ be an algebraically closed field of arbitrary characteristic. Let $A$ be an affine domain over $K$ with transcendence degree 1 which is not isomorphic to $K[x]$, and let $B$ be a domain over $K$. We show that the AK invariant distributes over the tensor product of $A$ by $B$. As a consequence, we obtain a generalization of the cancellation theorem of S. Abhyankar, P. Eakin, and W. Heinzer.

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Anthony J. Crachiola, Leonid Makar-Limanov. 2004-06-21. On the rigidity of small domains. https://arxiv.org/abs/math/0406412

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