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Localization of tight closure in two-dimensional rings

Kamran Divaani-Aazar·Massoud Tousi
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Abstract

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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Kamran Divaani-Aazar, Massoud Tousi. 2005-02-03. Localization of tight closure in two-dimensional rings. https://arxiv.org/abs/math/0502076

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