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A Note on the Weierstrass Preparation Theorem in Quasianalytic Local Rings

Published online by Cambridge University Press:  20 November 2018

Adam Parusiński  and
Jean-Philippe Rolin
Adam Parusiński
Affiliation:
Univ. Nice Sophia Antipolis, CNRS, LJAD, UMR 7351, 06100 Nice, France e-mail: [email protected]
Jean-Philippe Rolin
Affiliation:
Univ. de Bourgogne (Dijon), I.M.B., 9 av. A. Savary, BP47870, 21078 Dijon Cedex, France e-mail: [email protected]
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Abstract

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Consider quasianalytic local rings of germs of smooth functions closed under composition, implicit equation, and monomial division. We show that if the Weierstrass Preparation Theoremholds in such a ring, then all elements of it are germs of analytic functions.

Keywords

26E1026E0514P15Weierstrass Preparation Theoremquasianalytic local rings
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 57 , Issue 3 , 01 September 2014 , pp. 614 - 620
Copyright
Copyright © Canadian Mathematical Society 2014

References

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