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The hypersurface $ x + x^2y + z^2 + t^3 = 0$ over a field of arbitrary characteristic

Author: Anthony J. Crachiola
Journal: Proc. Amer. Math. Soc. 134 (2006), 1289-1298
MSC (2000): Primary 13A50; Secondary 14J30, 14R20
Published electronically: October 18, 2005
MathSciNet review: 2199171
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Abstract: We develop techniques for computing the AK invariant of domains with arbitrary characteristic. As an example, we show that for any field $ \mathbf{k}$ the ring $ \mathbf{k}[X,Y,Z,T] / (X + X^2 Y + Z^2 + T^3)$ is not isomorphic to a polynomial ring over $ \mathbf{k}$.

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Additional Information

Anthony J. Crachiola
Affiliation: Department of Mathematics and Computer Science, Loyola University, New Orleans, Louisiana 70118
Address at time of publication: Department of Mathematical Sciences, Saginaw Valley State University, 7400 Bay Road, University Center, Michigan 48710-0001

Keywords: AK invariant, additive group action, locally finite iterative higher derivation
Received by editor(s): August 25, 2004
Received by editor(s) in revised form: December 26, 2004
Published electronically: October 18, 2005
Dedicated: To Professor Leonid Makar-Limanov on the occasion of his sixtieth birthday
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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