Link between Noetherianity and the Weierstrass Division Theorem on some quasianalytic local rings
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- by Abdelhafed Elkhadiri
- Proc. Amer. Math. Soc. 140 (2012), 3883-3892
- DOI: https://doi.org/10.1090/S0002-9939-2012-11243-2
- 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.References
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Bibliographic Information
- Abdelhafed Elkhadiri
- Affiliation: Department of Mathematics, Faculty of Sciences, University Ibn Tofail, B.P. 133, Kénitra, Morocco
- Email: kabdelhafed@hotmail.com
- 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
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 3883-3892
- MSC (2010): Primary 26E10, 13F25, 32B05, 32B20; Secondary 03C10
- DOI: https://doi.org/10.1090/S0002-9939-2012-11243-2
- MathSciNet review: 2944729