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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Remarks on rings of constants of derivations


Author: Wei Li
Journal: Proc. Amer. Math. Soc. 107 (1989), 337-340
MSC: Primary 13N05; Secondary 12H05, 13B10
MathSciNet review: 979220
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Abstract: Let $ k$ be a field of characteristic $ p > 0$ and $ D \ne 0$ a family of $ k$-derivations of $ k[x,y]$. We prove that $ k{[x,y]^D}$ ,the ring of constants with respect to $ D$, is a free $ k[{x^p},{y^p}]$-module of rank $ p$ or 1 and $ k{[x,y]^D} = k[{x^p},{y^p},{f_1}, \ldots ,{f_{p - 1}}]$ for some $ {f_1}, \ldots ,{f_{p - 1}} \in k{[x,y]^D}$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0979220-9
PII: S 0002-9939(1989)0979220-9
Keywords: Derivations, rings of constants of derivations
Article copyright: © Copyright 1989 American Mathematical Society