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.
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