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Proceedings of the American Mathematical Society

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

 

 

On the purely inseparable closure of rings


Author: Shizuka Sato
Journal: Proc. Amer. Math. Soc. 100 (1987), 619-622
MSC: Primary 13B10; Secondary 13F25
DOI: https://doi.org/10.1090/S0002-9939-1987-0894426-3
MathSciNet review: 894426
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Abstract: Let $ K \subseteqq R$ be commutative rings with identity 1. Let $ D = \{ {D_i}\} $ be a higher derivation of $ R$. We shall prove in this paper that if $ K$ is invariant with respect to $ D$, the purely inseparable closure $ \overline {{K_R}} $ of $ K$ in $ R$ is invariant with respect to $ D$ and the formal power series ring $ \overline {{K_R}} [[t]]$ is purely inseparably closed in $ R[[t]]$.


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DOI: https://doi.org/10.1090/S0002-9939-1987-0894426-3
Keywords: Purely inseparable algebras, higher derivations
Article copyright: © Copyright 1987 American Mathematical Society