Link between Noetherianity and the Weierstrass Division Theorem on some quasianalytic local rings

Elkhadiri, Abdelhafed

doi:10.1090/S0002-9939-2012-11243-2

Link between Noetherianity and the Weierstrass Division Theorem on some quasianalytic local rings
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Proc. Amer. Math. Soc. 140 (2012), 3883-3892 Request permission

Abstract:

In the setting of well-behaved quasianalytic differentiable systems, we prove that the Weierstrass Division Theorem holds in such system if, and only if, the system is Noetherian.

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