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Galois extensions and the ramification sequence of some wildly ramified $ \pi $-adic fields


Authors: R. D. Davis and E. F. Wishart
Journal: Proc. Amer. Math. Soc. 30 (1971), 212-216
MSC: Primary 12.50
DOI: https://doi.org/10.1090/S0002-9939-1971-0282954-1
MathSciNet review: 0282954
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Abstract: In this paper the authors have found necessary and sufficient conditions for a pth degree Eisenstein extension of an arbitrary $ \pi $-adic field to be normal. In addition we have found where the Galois automorphisms must appear in the ramification sequence of the extended ring.


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

  • [1] R. Davis, On the inertial automorphisms of a class of ramified v-rings, Dissertation, Florida State University, Tallahassee, Fla., 1969.
  • [2] H. Hasse, Zahlentheorie, 2nd ed., Akademie-Verlag, Berlin, 1963. MR 27 #3621. MR 0153659 (27:3621)
  • [3] N. Heerema, Inertial automorphisms of a class of wildly ramified v-rings, Trans. Amer. Math. Soc. 132 (1968), 45-54. MR 36 #6407. MR 0223359 (36:6407)
  • [4] O. F. G. Schilling, The theory of valuations, Math. Surveys, no. 4, Amer. Math. Soc., Providence, R. I., 1950. MR 13, 315. MR 0043776 (13:315b)
  • [5] E. Wishart, Higher derivations on p-adic fields, Dissertation, Florida State University, Tallahassee, Fla., 1965.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0282954-1
Keywords: Eisenstein extension, ramification sequence, wildly ramified extension, normal extension, Galois automorphism
Article copyright: © Copyright 1971 American Mathematical Society

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