Remarks on rings of constants of derivations

Li, Wei

doi:10.1090/S0002-9939-1989-0979220-9

Remarks on rings of constants of derivations
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Proc. Amer. Math. Soc. 107 (1989), 337-340 Request permission

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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