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A short proof of the algebraic Weierstrass preparation theorem


Author: S. M. Gersten
Journal: Proc. Amer. Math. Soc. 88 (1983), 751-752
MSC: Primary 13J05; Secondary 32B05
DOI: https://doi.org/10.1090/S0002-9939-1983-0702313-2
MathSciNet review: 702313
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Abstract: The contraction mapping principle yields a short proof of the algebraic Weierstrass Preparation Theorem.


References [Enhancements On Off] (What's this?)

  • [B] N. Bourbaki, Éléments de mathématique. Fasc. XXXI. Algèbre commutative. Chapitre 7: Diviseurs, Actualités Scientifiques et Industrielles, No. 1314, Hermann, Paris, 1965 (French). MR 0260715
  • [K-K-O] D. Kreider, R. Kuller and D. Ostberg, Elementrary differential equations, Addison-Wesley, Reading, Mass., 1968.
  • [Z-S] Oscar Zariski and Pierre Samuel, Commutative algebra. Vol. II, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N. J.-Toronto-London-New York, 1960. MR 0120249

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0702313-2
Keywords: Complete local ring, distinguished polynomial, complete metric space, contraction mapping principle
Article copyright: © Copyright 1983 American Mathematical Society