Projective equivalence of ideals in Noetherian integral domains
| dc.creator | Heinzer, William J. | |
| dc.creator | Ratliff Jr, Louis J. | |
| dc.creator | Rush, David E. | |
| dc.date | 2007-12-05 | |
| dc.date.accessioned | 2026-07-07T08:47:36Z | |
| dc.date.available | 2026-07-07T08:47:36Z | |
| dc.description | Let I be a nonzero proper ideal in a Noetherian integral domain R. In this paper we establish the existence of a finite separable integral extension domain A of R and a positive integer m such that all the Rees integers of IA are equal to m. Moreover, if R has altitude one, then all the Rees integers of J = Rad(IA) are equal to one and the ideals J^m and IA have the same integral closure. Thus Rad(IA) = J is a projectively full radical ideal that is projectively equivalent to IA. In particular, if R is Dedekind, then there exists a Dedekind domain A having the following properties: (i) A is a finite separable integral extension of R; and (ii) there exists a radical ideal J of A and a positive integer m such that IA = J^m. | |
| dc.description | 20 pages | |
| dc.identifier | https://arxiv.org/abs/0712.0833 | |
| dc.identifier | http://arxiv.org/abs/0712.0833 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/143656 | |
| dc.subject | Commutative Algebra | |
| dc.title | Projective equivalence of ideals in Noetherian integral domains | |
| dc.type | text |