Note on the Weierstrass Preparation Theorem in Quasianalytic Local Rings

2013/03/18 by Jean-Philippe Rolin, Rolin, Jean-Philippe, Adam Parusiński +1 · 1 citation
Mathematics · #Advanced Topology and Set Theory #Rings, Modules, and Algebras #Functional Equations Stability Results

paper · doi:10.48550/arxiv.1303.4424

Abstract

Consider quasianalytic local rings of germs of smooth functions closed under composition, implicit equation, and monomial division. We show that if the Weierstrass Preparation Theorem holds in such a ring then all elements of it are germs of analytic functions. .

Citations

• The Field of Reals with Multisummable Series and the Exponential Function

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