Proceedings of the Edinburgh Mathematical Society (Series 2)

Research Article

Some results on test elements

Ian M. Aberbacha1* and Brian Maccrimmona1

a1 Department of Mathematics, University of Missouri, Columbia, MO 65211, U.S.A., E-mail address:

Let (R, m) be a Noetherian local reduced ring of positive prime characteristic. We show that if R is xs211A-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 xs211A-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