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On a generalization of test ideals
- Source :
- Nagoya Math. J. 175 (2004), 59-74
- Publication Year :
- 2004
- Publisher :
- Cambridge University Press (CUP), 2004.
-
Abstract
- 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 $t \ge 0$. We first prove a key lemma of this paper, 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 analog of so-called Skoda's theorem, which is formulated algebraically via adjoint ideals by Lipman in his proof of the "modified Brian\c{c}on--Skoda theorem."<br />Comment: 11 pages, AMS-LaTeX; v.2: minor changes, to appear in Nagoya Math. J
- Subjects :
- 13A35
Discrete mathematics
Lemma (mathematics)
Mathematics::Commutative Algebra
010308 nuclear & particles physics
General Mathematics
010102 general mathematics
Minimal ideal
Ideal norm
Mathematics - Commutative Algebra
Commutative Algebra (math.AC)
01 natural sciences
Combinatorics
Boolean prime ideal theorem
Principal ideal
0103 physical sciences
FOS: Mathematics
Exponent
Maximal ideal
0101 mathematics
Tight closure
Mathematics
Subjects
Details
- ISSN :
- 21526842 and 00277630
- Volume :
- 175
- Database :
- OpenAIRE
- Journal :
- Nagoya Mathematical Journal
- Accession number :
- edsair.doi.dedup.....bb7c983b42704cd8203a312f49432ac6