Intersections of symbolic powers of prime ideals

Details Intersections of symbolic powers of prime ideals Intersections of symbolic powers of prime ideals

2001-04-17

arxiv.org/abs/math/0104175v1

Mathematics

Commutative Algebra

29 pages

Scientific paper

Let (R,m) be a local ring with prime ideals p and q such that p+q is an m-primary ideal. If R is regular and contains a field, and dim(R/p)+dim(R/q)=dim(R), we prove that p^{(r)}\cap q^{(n)}\subseteq m^{m+n} for all positive integers r and s. This is proved using a generalization of Serre's Intersection Theorem which we apply to a hypersurface R/fR. The generalization gives conditions that guarantee that Serre's bound on the intersection dimension dim(R/p)+dim(R/q) \leq dim(R) holds when R is nonregular.

Affiliated with

Also associated with

No associations

Rating

Intersections of symbolic powers of prime ideals 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 Intersections of symbolic powers of prime ideals, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Intersections of symbolic powers of prime ideals will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-564512