- NAGOYA UNIV
The test ideal tau(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 tau(a(t)) associated to a given ideal a with rational exponent t greater than or equal to 0. We first prove a key lemma of this paper (Lemma 2.1), which gives a characterization of the ideal tau(a(t)). As applications of this key lemma, we generalize the preceding results on the behavior of the test ideal tau(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 Brianqon-Skoda theorem."
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