Failure of the Weierstrass Preparation Theorem in quasi-analytic   Denjoy-Carleman rings
  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. 
Francesca Acquistapace, Fabrizio Broglia, Michail Bronshtein, Andreea   Nicoara, Nahum Zobin
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