Failure of the Weierstrass Preparation Theorem in quasi-analytic Denjoy-Carleman rings
classification
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math.AG
keywords
theoremdenjoy-carlemanpreparationquasi-analyticringsweierstrassfailfailure
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It is shown that Denjoy-Carleman quasi-analytic rings of germs of functions in two or more variables fail to satisfy the Weierstrass Preparation Theorem. The result is proven via a non-extension theorem.
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