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math.CA2012★ 10 cited
Failure of the Weierstrass Preparation Theorem in quasi-analytic Denjoy-Carleman rings
Francesca Acquistapace, Fabrizio Broglia, Michail Bronshtein +2
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…
math.AG2012★ 8 cited
A Nullstellensatz for Łojasiewicz ideals
Francesca Acquistapace, Fabrizio Broglia, Andreea Nicoara
For an ideal of smooth functions that is either Łojasiewicz or weakly Łojasiewicz, we give a complete characterization of the ideal of functions vanishing on its variety in terms o…