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Proceedings of the American Mathematical Society

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

 

 

Differential basis, $ p$-basis, and smoothness in characteristic $ p>0$


Author: Andrzej Tyc
Journal: Proc. Amer. Math. Soc. 103 (1988), 389-394
MSC: Primary 13B99
MathSciNet review: 943051
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Abstract: It is shown that every differential basis of a Noetherian ring $ R$ of prime characteristic $ p$ over an arbitrary subring $ k$ is a $ p$-basis of $ R$ over $ k$. Moreover, if $ k$ is a field, then $ R$ is smooth over $ k$, provided $ R$ has a differential basis over $ k$ and the ring $ R{ \otimes _k}{k^{{p^{ - 1}}}}$ is reduced.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0943051-5
Article copyright: © Copyright 1988 American Mathematical Society