Some Results on Tight Closure and Completion

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 (PÁ)* ≠ P*Á. 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.