TY - JOUR
T1 - On a generalization of test ideals
AU - Hara, Nobuo
AU - Takagi, Shunsuke
N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2004/9
Y1 - 2004/9
N2 - 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.".
AB - 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.".
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U2 - 10.1017/s0027763000008904
DO - 10.1017/s0027763000008904
M3 - Article
AN - SCOPUS:10244225376
VL - 175
SP - 59
EP - 74
JO - Nagoya Mathematical Journal
JF - Nagoya Mathematical Journal
SN - 0027-7630
ER -