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

DOI10.1090/S0002-9939-2012-11243-2zbMath1278.26024MaRDI QIDQ2846743

Abdelhafed El Khadiri

Publication date: 3 September 2013

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Noetherian ringsWeierstrass division theoremquasianalytic rings

Mathematics Subject Classification ID

(C^infty)-functions, quasi-analytic functions (26E10) Semi-analytic sets, subanalytic sets, and generalizations (32B20) Formal power series rings (13F25) Quantifier elimination, model completeness, and related topics (03C10) Analytic algebras and generalizations, preparation theorems (32B05)

Related Items

ON DIVISION OF QUASIANALYTIC FUNCTION GERMS ⋮ Solutions of some quasianalytic equations

Cites Work

• When \(\varphi(f)\) convergent implies \(f\) is convergent
• Algèbre locale. Multiplicités. Cours au Collège de France, 1957-1958, rédigé par Pierre Gabriel. 2e ed.
• Idéaux de fonctions différentiables. I
• Homomorphism of quasianalytic local rings
• Weierstrass Division in Quasianalytic Local Rings
• Infinite Differentiability in Polynomially Bounded O-Minimal Structures
• Weierstrass division theorem in quasianalytic local rings
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