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We introduce a new variant of tight closure associated to any fixed ideal a, which we call a-tight closure, and study various properties thereof. In our theory, the annihilator ideal τ(a) of all a-tight closure relations, which is a generalization of the test ideal in the usual tight closure theory, plays a particularly important role. We prove the… (More)

- NOBUO HARA
- 2001

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)

- NOBUO HARA
- 2008

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)

- Nobuo Hara, Paul Monsky, NOBUO HARA
- 2006

Using an argument based on an idea of Monsky, we prove the rationality of the F-pure thresholds of curve singularities on a smooth surface defined over a finite field. More generally, we prove in this setting the rationality and discreteness of F-jumping exponents, the smallest positive one of which is the F-pure threshold. We also give a lower bound for… (More)

- Nobuo Hara, Hidenori Ohashi, Taichi Ito, Takeo Yamaguchi
- The journal of physical chemistry. B
- 2009

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)

- Nobuo Hara
- 2007

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)

- NOBUO HARA
- 2008

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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