Some Results On Normal Homogeneous Ideals
| dc.creator | Reid, Les | |
| dc.creator | Roberts, Leslie G. | |
| dc.creator | Vitulli, Marie A. | |
| dc.date | 2002-09-22 | |
| dc.date.accessioned | 2026-07-07T04:51:06Z | |
| dc.date.available | 2026-07-07T04:51:06Z | |
| dc.description | In this article we investigate when a homogeneous ideal in a graded ring is normal, that is, when all positive powers of the ideal are integrally closed. We are particularly interested in homogeneous ideals in an N-graded ring generated by all homogeneous elements of degree at least m and monomial ideals in a polynomial ring over a field. For ideals of the first trype we generalize a recent result of S. Faridi. We prove that a monomial ideal in a polynomial ring in n indeterminates over a field is normal if and only if the first n-1 positive powers of the ideal are integrally closed. We then specialize to the case of ideals obtained by taking integral closures of m-primary ideals generated by powers of the variables. We obtain classes of normal monomial ideals and arithmetic critera for deciding when the monomial ideal is not normal. | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/math/0209285 | |
| dc.identifier | http://arxiv.org/abs/math/0209285 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65029 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 13C13, 13A20 | |
| dc.title | Some Results On Normal Homogeneous Ideals | |
| dc.type | text |