TEST IDEALS IN LOCAL-RINGS

It is shown that certain aspects of the theory of tight closure are well behaved under localization. Let J be the parameter test ideal for R, a complete local Cohen-Macaulay ring of positive prime characteristic. For any multiplicative system U subset of R, it is shown that JU(-1)R is the parameter test ideal for U(-1)R. This is proved by proving more general localization results for the here-introduced classes of ''F-ideals'' of R and ''F-submodules of the canonical module'' of R, which are annihilators of R modules with an action of Frobenius. It also follows that the parameter test ideal cannot be contained in any parameter ideal of R.