A criterion for $p$-closedness of derivations in dimension two

Kentaro Mitsui, Nobuo Sato
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Abstract

Jacobson developed a counterpart of Galois theory for purely inseparable field extensions in positive characteristic. In his theory, a certain type of derivations replace the role of the generators of Galois groups. This article provides a convenient criterion for determining such derivations in dimension two. We also present examples demonstrating the efficiency of our criterion.
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二维导数的$p$封闭性标准
雅各布森为正特征的纯不可分场扩展提出了伽罗瓦理论的对应理论。在他的理论中,某类衍生取代了伽罗瓦群的生成器的作用。本文提供了一个方便的判据,用于确定二维中的这类衍生。我们还举例说明了我们的准则的效率。
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