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Normal basis for an ideal in a local ring

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Abstract

An effective construction is given for a normal ideal basis (when it exists) in local number field extensions with higher ramification.

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Literature cited

  1. 1.

    E. Noether, “Normalbasis bei Körpern ohne höher Verzweigung,” J. Reine Angew. Math.,167, 147–152 (1932).

  2. 2.

    S. Ullom, “Integral and normal bases in Galois extensions of local fields,” Nagoya Math. J.,39, 141–148 (1970).

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    J.-P. Serre, Corps Locaux, Paris (1962).

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    V. D. Lesev, “On a theorem of E. Noether,” Uch. Zap. Kabardino-Balkarsk. Univ., Ser. Fiz. Mat., No. 13, 92–95 (1966).

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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 64, pp. 64–68, 1976.

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Vostokov, S.V. Normal basis for an ideal in a local ring. J Math Sci 17, 1755–1758 (1981). https://doi.org/10.1007/BF01091761

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Keywords

  • Local Ring
  • Number Field
  • Field Extension
  • Normal Basis
  • Local Number