Kernels of derivations in positive characteristic

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概要

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• Let $R$ be an integral domain that is finitely generated over a field $k$.Let $D : R \to R$ be a derivation over $k$. Our aim is to compute $\ker D$.Under the assumptions that the characteristic of $k$ is zero,$D$ is locally nilpotent and $\ker D$ is finitely generated over $k$,Essen gave an explicit algorithm based on the exponential of the derivation.In this paper we give an analogous algorithm in the positive characteristic caseusing a truncated version of the exponential. It does not require the nilpotence of $D$.We give several computational examples of application of our algorithm.Also using higher derivations, we obtain a word-by-word translation of Essen's formulato positive characteristics.

• 広島大学の論文

著者

• Okuda Shun-ichiro

  Department of Mathematics, Graduate School of Science, Hiroshima University

• Okuda Shun-ichiro

  Department Of Mathematics Graduate School Of Science Hiroshima University

関連論文

• Positive characteristic approach to Weak Kernel Conjecture
• Kernels of derivations in positive characteristic

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