On high order derivations of fields
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- by J. N. Mordeson and B. Vinograde PDF
- Proc. Amer. Math. Soc. 32 (1972), 421-422 Request permission
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
- J. N. Mordeson and B. Vinograde, Exponents and intermediate fields of purely inseparable extensions, J. Algebra 17 (1971), 238–242. MR 288106, DOI 10.1016/0021-8693(71)90031-7
- John N. Mordeson and Bernard Vinograde, Structure of arbitrary purely inseparable extension fields, Lecture Notes in Mathematics, Vol. 173, Springer-Verlag, Berlin-New York, 1970. MR 0276204
- Yoshikazu Nakai, High order derivations. I, Osaka Math. J. 7 (1970), 1–27. MR 263804
- Yoshikazu Nakai, Kôtaro Kosaki, and Yasunori Ishibashi, High order derivations. II, J. Sci. Hiroshima Univ. Ser. A-I Math. 34 (1970), 17–27. MR 266905
Additional Information
- © Copyright 1972 American Mathematical Society
- 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