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.)