Intersections of symbolic powers of prime ideals
| dc.creator | Sather-Wagstaff, Sean | |
| dc.date | 2001-04-17 | |
| dc.date.accessioned | 2026-07-07T06:26:43Z | |
| dc.date.available | 2026-07-07T06:26:43Z | |
| dc.description | 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. | |
| dc.description | 29 pages | |
| dc.identifier | https://arxiv.org/abs/math/0104175 | |
| dc.identifier | http://arxiv.org/abs/math/0104175 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/97190 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13H05; 13H15; 13C15; 13D22 | |
| dc.title | Intersections of symbolic powers of prime ideals | |
| dc.type | text |