Localization of tight closure in two-dimensional rings
classification
🧮 math.AC
keywords
closurelocalizationprimeringtightcharacteristiccommutesdimensional
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It is shown that tight closure commutes with localization in any two dimensional ring $R$ of prime characteristic if either $R$ is a Nagata ring or $R$ possesses a weak test element. Moreover, it is proved that tight closure commutes with localization at height one prime ideals in any ring of prime characteristic.
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