a1 Department of Mathematics, University of Missouri, Columbia, MO 65211, U.S.A., E-mail address: email@example.com
Let (R, m) be a Noetherian local reduced ring of positive prime characteristic. We show that if R is -Gorenstein then the test ideal of R localizes, which extends a result of K. E. Smith. We also show that if Rc, is weakly F-regular and -Gorenstein, then c has a power which is a completely stable test element. This extends results of Höchster and Huneke.
(Received September 24 1997)
* The first author was partially supported by the NSF and by the University of Missouri Research Board