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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Remarks on rings of constants of derivations
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by Wei Li PDF
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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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 107 (1989), 337-340
  • MSC: Primary 13N05; Secondary 12H05, 13B10
  • DOI: https://doi.org/10.1090/S0002-9939-1989-0979220-9
  • MathSciNet review: 979220