Abstract
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(at) associated to a given ideal a with rational exponent t ≥ 0. We first prove a key lemma of this paper (Lemma 2.1), which gives a characterization of the ideal τ (at). As applications of this key lemma, we generalize the preceding results on the behavior of the test ideal τ(R). Moreover, we prove an analogue of so-called Skoda's theorem, which is formulated algebraically via adjoint ideals by Lipman in his proof of the "modified Briançon-Skoda theorem.".
Original language | English |
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Pages (from-to) | 59-74 |
Number of pages | 16 |
Journal | Nagoya Mathematical Journal |
Volume | 175 |
DOIs | |
Publication status | Published - 2004 Sept |
Externally published | Yes |
ASJC Scopus subject areas
- Mathematics(all)