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Constants of derivations in polynomial rings over unique factorization domains

Author: M'hammed El Kahoui
Journal: Proc. Amer. Math. Soc. 132 (2004), 2537-2541
MSC (2000): Primary 12H05, 13P10
Published electronically: April 8, 2004
MathSciNet review: 2054777
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Abstract: A well-known theorem, due to Nagata and Nowicki, states that the ring of constants of any ${\mathcal K}$-derivation of ${\mathcal K}[x,y]$, where ${\mathcal K}$ is a commutative field of characteristic zero, is a polynomial ring in one variable over ${\mathcal K}$. In this paper we give an elementary proof of this theorem and show that it remains true if we replace ${\mathcal K}$ by any unique factorization domain of characteristic zero.

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Additional Information

M'hammed El Kahoui
Affiliation: Department of Mathematics, Faculty of Sciences Semlalia, Cadi Ayyad University, P.O. Box 2390, Marrakech, Morocco

Keywords: Derivations, ring of constants
Received by editor(s): December 27, 2002
Received by editor(s) in revised form: April 1, 2003
Published electronically: April 8, 2004
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2004 American Mathematical Society