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Abstract
Recently, Brenner and Monsky found an example of an ideal in a hypersurface ring whose tight closure does not commute with localization, thus answered the localization problem in tight closure theory in the negative. In this article, we use Monsky's calculations to analyze the set of associated primes of the Frobenius powers of this ideal and show that this set is infinite.
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ACKNOWLEDGMENT
We thank Hailong Dao for useful conversations regarding the proof of Theorem 3.17, and Paul Monsky for kindly sending us a preprint of his work [Citation6]. The result of this paper is part of the author's doctoral thesis at the University of Utah, and the author would like to thank Paul Roberts for his financial support. The author is partially supported by NAFOSTED 101.01-2011.37 (Vietnam).
Notes
Communicated by S. Goto.