**Graded Annihilators and Uniformly ***F*-Compatible Ideals

*Rodney Y. Sharp*

*F*-Compatible Ideals

**Abstract**

Let *R* be a commutative (Noetherian) local ring of prime characteristic *p* that is *F*-pure. This paper is concerned with comparison of three finite sets of radical ideals of *R*, one of which is only defined in the case when *R* is *F*-finite (that is, is finitely generated when viewed as a module over itself via the Frobenius homomorphism). Two of the afore-mentioned three sets have links to tight closure, via test ideals. Among the aims of the paper are a proof that two of the sets are equal, and a proposal for a generalization of I. M. Aberbach’s and F. Enescu’s splitting prime.