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We study tight closure and test ideals in rings of characteristic p 0 using resolution of singularities. The notions of F -rational and F regular rings are defined via tight closure, and they are known to correspond with rational and log terminal singularities, respectively. In this paper, we reformulate this correspondence by means of the notion of the(More)
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) 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(a).(More)
We found that protons rapidly conduct through unfreezable and bound water in a pore-filling electrolyte membrane (PF-membrane), although many ions usually conduct through free water contained in polymer electrolytes. PF-membrane is a unique membrane that can suppress the swelling of filled sulfonated poly(arylene ether sulfone) (SPES) because of its rigid(More)
Let R be a Noetherian commutative ring containing a eld. The test ideal, introduced by Hochster and Huneke in HH1], has emerged as an important object associated to R. The test ideal can be deened as the largest ideal J of R such that JI I for all ideals I of R where I denotes the tight closure of I. Although it is not obvious that a ring R admits a(More)
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) 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(a).(More)
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