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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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Article copyright: © Copyright 1986 American Mathematical Society