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

 

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


Author: Abdelhafed Elkhadiri
Journal: Proc. Amer. Math. Soc. 140 (2012), 3883-3892
MSC (2010): Primary 26E10, 13F25, 32B05, 32B20; Secondary 03C10
Published electronically: March 20, 2012
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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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Additional Information

Abdelhafed Elkhadiri
Affiliation: Department of Mathematics, Faculty of Sciences, University Ibn Tofail, B.P. 133, Kénitra, Morocco
Email: kabdelhafed@hotmail.com

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11243-2
PII: S 0002-9939(2012)11243-2
Keywords: Quasianalytic rings, Weierstrass Division Theorem, Noetherian rings
Received by editor(s): January 4, 2011
Received by editor(s) in revised form: May 9, 2011
Published electronically: March 20, 2012
Additional Notes: This work was partially supported by PARS MI33
Communicated by: Franc Forstneric
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.