On the rigidity of small domains

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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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Commutative Algebra, Algebraic Geometry, 13A50; 14R10

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http://salesiana.dossiersoluciones.com/handle/123456789/71628

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0406412
 http://arxiv.org/abs/math/0406412

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arXiv