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Weierstrass Division in Quasianalytic Local Rings

Published online by Cambridge University Press:  20 November 2018

C. L. Childress
C. L. Childress*
Affiliation:
Case Western Reserve University, Cleveland, Ohio
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In this paper we consider the problem of extending the Weierstrass division theorem to quasianalytic local rings of germs of functions of k real variables which properly contain the local ring of germs of analytic functions. After some background material (§ 2) and some technical preliminaries (§ 3), we show by examples that the so-called generic division theorem fails in such rings if k ≧ 1 and that the Weierstrass division theorem fails in such rings if k ≧ 2 (§ 4).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 5 , 01 October 1976 , pp. 938 - 953
Copyright
Copyright © Canadian Mathematical Society 1976

References

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