Differential basis and 𝑝-basis of a regular local ring

Kimura, Tetsuzo; Niitsuma, Hiroshi

doi:10.1090/S0002-9939-1984-0759648-8

Differential basis and $p$-basis of a regular local ring
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by Tetsuzo Kimura and Hiroshi Niitsuma

Proc. Amer. Math. Soc. 92 (1984), 335-338

DOI: https://doi.org/10.1090/S0002-9939-1984-0759648-8

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Abstract:

We prove that any differential basis of a regular local ring $R$ of characteristic $p > 0$ over ${R^p}$ is a $p$-basis of $R$ over ${R^p}$. This result gives a characterization of a regular local ring $R$ which has a $p$-basis over ${R^p}$.

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