Strong F-regularity in images of regular rings

Abstract

Abstract. We characterize strong F-regularity, a property associated with tight closure, in a large class of rings. A special case of our results is a workable criterion in complete intersection rings.

The lower semicontinuity of the Frobenius splitting numbers

“…So, it is enough to check the equality s e (R) • q dim(R) = λ S S n [q] :(I [q] :I) under the additional hypothesis that R is F-finite and this is observed in [2] (see the remarks immediately after [2, Theorem 4.2]). (The reader might be also interested in [5,6]. )…”

F-singularities of pairs and Inversion of Adjunction of arbitrary codimension

“…Proof. The proof is similar to those in [5], [6] and [10]. We may assume without loss of generality that (R, m) is a d-dimensional complete regular local ring.…”

Strong F-regularity and generating morphisms of local cohomology modules

“…The central result of the present paper, Theorem 4.6, provides an effective test for the strong F -regularity of a (non-Gorenstein) Cohen-Macaulay reduced complete local domain A of dimension at least 2, containing a perfect field of positive characteristic. As we point out in Remark 4.8, it affords a structural similarity with the characterization given in [12]. We apply the theorem in the case where A is the determinantal ring defined by the minors of order 2 of a 3 × 3 generic symmetric matrix over a field of characteristic 2 or 3 (Example 4.9).…”