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A note on Hensel's lemma in several variables

Author(s): Benji Fisher
Journal: Proc. Amer. Math. Soc. 125 (1997), 3185-3189.
MSC (1991): Primary 13J15; Secondary 13J05, 13B40
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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:

[B1]: N. Bourbaki, Algèbre, Hermann, Paris, 1959.
[B2]: -, Algèbre Commutative, Hermann, Paris, 1962.
[Da-F]: R. Dabrowski and B. Fisher, A stationary-phase formula for exponential sums over $\mathbb {Z}/p^{m}\mathbb {Z}$ and applications to $\operatorname {GL}(3)$ -Kloosterman sums, Acta. Arith. (to appear).
[Gr]: M. J. Greenberg, Rational points in Henselian discrete valuation rings, Pub. Math. IHES 31 (1966), 59-64. MR 34:7515
[R]: M. Raynaud, Anneaux Locaux Henseliens, Lecture Notes in Math. 169, Springer-Verlag, Berlin-Heidelberg-New York, 1970. MR 43:3252

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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

DOI: 10.1090/S0002-9939-97-04112-9
PII: S 0002-9939(97)04112-9
Keywords: Hensel's lemma, power series, Henselian rings
Received by editor(s): May 20, 1996
Communicated by: Wolmer V. Vasconcelos
Copyright of article: Copyright 1997, American Mathematical Society


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