Abstract

"symbolic blow-up", (~ P(n)=S a Noetherian ring? If S is Noetherian and dim n 0 RIP=l, Cowsik observed that P must be a set-theoretic complete intersection. If R is not regular, there is no hope in general of S being Noetherian. In fact if R is any normal two dimensional local ring and P is a height one prime ideal of R which is not torsion in the class group of R, then S is never Noetherian. This idea is behind the Rees counterexample [6] to the generalized Zariski question. As far as the author knows, there are no known counter examples to the question of Cowsik. The most trivial case is the following: if R is Nagata and

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.