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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
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:
- [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
 and applications to  -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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