Localization of tight closure in two-dimensional rings

Details Localization of tight closure in two-dimensional rings Localization of tight closure in two-dimensional rings

2005-02-03

arxiv.org/abs/math/0502076v1

Mathematics

Commutative Algebra

7 pages, to appear in Proc. Indian Acad. Sci. (Math. Sci.)

Scientific paper

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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