The concept of F-purity was introduced by Hochster and Roberts [6]; the F-purity for a Noetherian ring of prime characteristic is equivalent to the splitting of the Frobenius map when the ring is finitely generated over its subring of pth powers. It is closely related to the Frobenius splitting property a la Mehta and Ramanathan [11] for algebraic varieties; more precisely, the F-split property for an irreducible projective variety X over an algebraically closed field of positive characteristic is equivalent to the F-purity of the ring ⊕_(n≥0) H~0(X; L~n) for any ample line bundle L over X (cf. [3; 13; 14]). We feel that it is only appropriate to dedicate this paper to Professor Hochster on the occasion of his sixty-fifth birthday and thus make a modest contribution to this birthday volume.
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