Let k be an algebraically closed field of arbitrary characteristic. We give a self-contained algebraic proof of the following statement: IfThis fact, which is due to Fujita, Miyanishi, Sugie, and Russell, solves the Zariski cancellation problem for surfaces. To achieve our proof, we first show that if A is a finitely generated domain with AK( A) = A, then AK( A[x]) = A.
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. ο 2004 Elsevier Inc. All rights reserved.
Abstract. We develop techniques for computing the AK invariant of a domain with arbitrary characteristic. We use these techniques to describe for any field k the automorphism group of k[X, Y, Z]/(X n Y β Z 2 β h(X)Z), where h(0) = 0 and n β₯ 2, as well as the isomorphism classes of these algebras.
Abstract. We develop techniques for computing the AK invariant of domains with arbitrary characteristic. As an example, we show that for any field k theis not isomorphic to a polynomial ring over k.
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