On a generalization of test ideals

Nobuo Hara, Shunsuke Takagi

Research output: Contribution to journalArticlepeer-review

56 Citations (Scopus)


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 languageEnglish
Pages (from-to)59-74
Number of pages16
JournalNagoya Mathematical Journal
Publication statusPublished - 2004 Sept
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)


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