paper

Localization of tight closure in two-dimensional rings

arXiv:math/0502076

Abstract

It is shown that tight closure commutes with localization in any two dimensional ring of prime characteristic if either is a Nagata ring or 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.

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

Localization of tight closure in two-dimensional rings · wovepaper