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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Power series and smooth functions equivalent to a polynomial


Author: Wojciech Kucharz
Journal: Proc. Amer. Math. Soc. 98 (1986), 527-533
MSC: Primary 32B05; Secondary 58C25
MathSciNet review: 857956
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Abstract: An algebraic criterion is given for a power series in $ n$ variables over a field of characteristic 0 to be equivalent to a polynomial in $ n - k$ variables over the ring of power series in $ k$ variables. For convergent power series over the reals or complexes a geometric interpretation of the criterion is established. An analogous sufficient condition is obtained for germs of smooth functions. Most of the previously known results follow easily from the criterion.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0857956-5
PII: S 0002-9939(1986)0857956-5
Article copyright: © Copyright 1986 American Mathematical Society