# On the rigidity of small domains

Research paper by Anthony J. Crachiola, Leonid Makar-Limanov

Indexed on: 21 Jun '04Published on: 21 Jun '04Published in: Mathematics - Commutative Algebra

#### 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.