Constants of derivations in polynomial rings over unique factorization domains

El Kahoui, M’hammed

doi:10.1090/S0002-9939-04-07313-7

Constants of derivations in polynomial rings over unique factorization domains
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by M’hammed El Kahoui

Proc. Amer. Math. Soc. 132 (2004), 2537-2541

DOI: https://doi.org/10.1090/S0002-9939-04-07313-7

Published electronically: April 8, 2004

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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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