Non-Noetherianity of Denjoy-Carleman rings of germs
Algebraic Geometry
2014-10-16 v2 Classical Analysis and ODEs
Abstract
It is shown that Denjoy-Carleman quasi analytic rings of germs of functions in two or more variables either complex or real valued that are stable under derivation and strictly larger than the ring of real-analytic germs are not Noetherian rings. The failure of Weierstrass division on these Denjoy-Carleman classes yields a contradiction to Noetherianity via a stronger version of Artin Approximation due to Popescu as well as results on projective modules. This settles a 35-year old open problem in real algebraic geometry.
Keywords
Cite
@article{arxiv.1108.0036,
title = {Non-Noetherianity of Denjoy-Carleman rings of germs},
author = {Liat Kessler and Andreea C. Nicoara},
journal= {arXiv preprint arXiv:1108.0036},
year = {2014}
}
Comments
Paper withdrawn due to error in case 2.1