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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A note on Hensel’s lemma in several variables
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by Benji Fisher PDF
Proc. Amer. Math. Soc. 125 (1997), 3185-3189 Request permission

Abstract:

The standard hypotheses for Hensel’s Lemma in several variables are slightly stronger than necessary, in the case that the Jacobian determinant is not a unit. This paper shows how to weaken the hypotheses for Hensel’s Lemma and some related theorems.
References
  • N. Bourbaki, Algèbre, Hermann, Paris, 1959.
  • —, Algèbre Commutative, Hermann, Paris, 1962.
  • R. Dabrowski and B. Fisher, A stationary-phase formula for exponential sums over $\mathbb {Z} /p^{m}\mathbb {Z}$ and applications to $\mathrm {GL} (3)$-Kloosterman sums, Acta. Arith. (to appear).
  • Marvin J. Greenberg, Rational points in Henselian discrete valuation rings, Inst. Hautes Études Sci. Publ. Math. 31 (1966), 59–64. MR 207700
  • Michel Raynaud, Anneaux locaux henséliens, Lecture Notes in Mathematics, Vol. 169, Springer-Verlag, Berlin-New York, 1970 (French). MR 0277519
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Additional Information
  • Benji Fisher
  • Affiliation: Department of Mathematics, Columbia University, New York, New York 10027
  • Address at time of publication: The Bronx High School of Science, 75 West 205$^{\mathrm {th}}$ Street, Bronx, New York 10468
  • Email: benji@math.columbia.edu
  • Received by editor(s): May 20, 1996
  • Communicated by: Wolmer V. Vasconcelos
  • © Copyright 1997 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 125 (1997), 3185-3189
  • MSC (1991): Primary 13J15; Secondary 13J05, 13B40
  • DOI: https://doi.org/10.1090/S0002-9939-97-04112-9
  • MathSciNet review: 1422869