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On high order derivations of fields


Authors: J. N. Mordeson and B. Vinograde
Journal: Proc. Amer. Math. Soc. 32 (1972), 421-422
MSC: Primary 12.45
DOI: https://doi.org/10.1090/S0002-9939-1972-0289466-0
MathSciNet review: 0289466
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Abstract: Let $ \mathcal{D}(L/K)$ denote the derivation algebra of a field extension $ L/K$ of prime characteristic. If $ L/K$ is purely inseparable and has an exponent, then every intermediate field F of $ L/K$ equals the center of $ \mathcal{D}(L/F)$. Here we prove the converse of this statement.


References [Enhancements On Off] (What's this?)

  • [1] J. Mordeson and B. Vinograde, Exponents and intermediate fields of purely inseparable extensions, J. Algebra 17 (1971), 238-242. MR 0288106 (44:5304)
  • [2] -, Structure of arbitrary purely inseparable extension fields, Lecture Notes in Math., Vol. 173, Springer-Verlag, New York, 1970. MR 0276204 (43:1952)
  • [3] Y. Nakai, High order derivations. I, Osaka J. Math. 7 (1970), 1-27. MR 41 #8404. MR 0263804 (41:8404)
  • [4] Y. Nakai, K. Kosaki and Y. Ishibashi, High order derivations. II, J. Sci. Hiroshima Univ. Ser. A-I Math. 34 (1970), 17-27. MR 42 #1807. MR 0266905 (42:1807)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0289466-0
Keywords: High order derivations, field extension, purely inseparable, relative p-base
Article copyright: © Copyright 1972 American Mathematical Society

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