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A note on Hensel’s lemma in several variables

Author: Benji Fisher
Journal: Proc. Amer. Math. Soc. 125 (1997), 3185-3189
MSC (1991): Primary 13J15; Secondary 13J05, 13B40
MathSciNet review: 1422869
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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 [Enhancements On Off] (What's this?)

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  • 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
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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

Keywords: Hensel’s lemma, power series, Henselian rings
Received by editor(s): May 20, 1996
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 1997 American Mathematical Society