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A note on the weierstrass preparation theorem in quasianalytic local rings

Canadian Mathematical Bulletin (2014) 57(3) 614-620
DOI: 10.4153/CMB-2013-034-5
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Abstract

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

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Parusiński, A., & Rolin, J. P. (2014). A note on the weierstrass preparation theorem in quasianalytic local rings. Canadian Mathematical Bulletin, 57(3), 614–620. https://doi.org/10.4153/CMB-2013-034-5

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