Non-Noetherianity of Denjoy-Carleman rings of germs

Details Non-Noetherianity of Denjoy-Carleman rings of germs Non-Noetherianity of Denjoy-Carleman rings of germs

2011-07-30

arxiv.org/abs/1108.0036v1

Mathematics

Algebraic Geometry

19 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Non-Noetherianity of Denjoy-Carleman rings of germs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Non-Noetherianity of Denjoy-Carleman rings of germs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Non-Noetherianity of Denjoy-Carleman rings of germs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-135940