On a generalization of test ideals
| dc.creator | Hara, Nobuo | |
| dc.creator | Takagi, Shunsuke | |
| dc.date | 2002-10-09 | |
| dc.date | 2003-12-03 | |
| dc.date.accessioned | 2026-07-07T04:51:46Z | |
| dc.date.available | 2026-07-07T04:51:46Z | |
| dc.description | The test ideal $τ(R)$ of a ring $R$ of prime characteristic is an important object in the theory of tight closure. In this paper, we study a generalization of the test ideal, which is the ideal $τ(\a^t)$ associated to a given ideal $\a$ with rational exponent $t \ge 0$. We first prove a key lemma of this paper, which gives a characterization of the ideal $τ(\a^t)$. As applications of this key lemma, we generalize the preceding results on the behavior of the test ideal $τ(R)$. Moreover, we prove an analog of so-called Skoda's theorem, which is formulated algebraically via adjoint ideals by Lipman in his proof of the "modified Briançon--Skoda theorem." | |
| dc.description | 11 pages, AMS-LaTeX; v.2: minor changes, to appear in Nagoya Math. J | |
| dc.identifier | https://arxiv.org/abs/math/0210131 | |
| dc.identifier | http://arxiv.org/abs/math/0210131 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65226 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13A35 | |
| dc.title | On a generalization of test ideals | |
| dc.type | text |