Failure of the Weierstrass Preparation Theorem in quasi-analytic Denjoy-Carleman rings
arXiv:1212.4265 · doi:10.1016/j.aim.2014.03.002
Abstract
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.
17 pages; accepted at the Advances in Mathematics