Some results on tight closure and completion

[摘要] We construct two examples of nonexcellent local Noetherian domains which demonstrate that tight closure and completion do not commute. The first example is a local normal domain A with a height one principal prime ideal P such that (P (A) over cap)* not equal P*(A) over cap. We also construct an example of a complete local normal Gorenstein domain which is not F-regular but is the completion of an F-regular local ring. (C) 2001 Elsevier Science.

[发布日期] 2001-12-15