Test ideals in diagonal hypersurface rings II
| dc.creator | McDermott, Moira A. | |
| dc.date | 2002-07-12 | |
| dc.date | 2002-12-30 | |
| dc.date.accessioned | 2026-07-07T04:49:39Z | |
| dc.date.available | 2026-07-07T04:49:39Z | |
| dc.description | Let $R=k[x_1, ..., x_n]/(x_1^d + ... + x_n^d)$, where $k$ is a field of characteristic $p$, $p$ does not divide $d$ and $n \geq 3$. We describe a method for computing the test ideal for these diagonal hypersurface rings. This method involves using a characterization of test ideals in Gorenstein rings as well as developing a way to compute tight closures of certain ideals despite the lack of a general algorithm. In addition, we compute examples of test ideals in diagonal hypersurface rings of small characteristic (relative to $d$) including several that are not integrally closed. These examples provide a negative answer to Smith's (2000, Comm. in Alg.) question of whether the test id eal in general is always integrally closed. | |
| dc.description | revised version, incorporating referee's comments, LaTeX, 10 pages | |
| dc.identifier | https://arxiv.org/abs/math/0207109 | |
| dc.identifier | http://arxiv.org/abs/math/0207109 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64503 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13A35 | |
| dc.title | Test ideals in diagonal hypersurface rings II | |
| dc.type | text |