Strong F-regularity in images of regular rings

Glassbrenner, Donna

doi:10.1090/S0002-9939-96-03030-4

Strong F-regularity in images of regular rings
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by Donna Glassbrenner

Proc. Amer. Math. Soc. 124 (1996), 345-353

DOI: https://doi.org/10.1090/S0002-9939-96-03030-4

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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.

References

Richard Fedder, $F$-purity and rational singularity, Trans. Amer. Math. Soc. 278 (1983), no. 2, 461–480. MR 701505, DOI 10.1090/S0002-9947-1983-0701505-0
Richard Fedder and Keiichi Watanabe, A characterization of $F$-regularity in terms of $F$-purity, Commutative algebra (Berkeley, CA, 1987) Math. Sci. Res. Inst. Publ., vol. 15, Springer, New York, 1989, pp. 227–245. MR 1015520, DOI 10.1007/978-1-4612-3660-3_{1}1
N. Hara, F-regularity and F-purity of graded rings, J. Algebra (to appear).
M. Hochster, Tight closure in equal characteristic, big Cohen-Macaulay algebras and solid closure, Special Talk, AMS Summer research conference, Mount Holyoke, July 6, 1992.
Melvin Hochster and Craig Huneke, Tight closure, invariant theory, and the Briançon-Skoda theorem, J. Amer. Math. Soc. 3 (1990), no. 1, 31–116. MR 1017784, DOI 10.1090/S0894-0347-1990-1017784-6
—, Tight closures of parameter ideals and splitting in module-finite extensions, preprint.
—, F-regularity, test elements, and smooth base change, preprint.
Melvin Hochster and Craig Huneke, Tight closure and strong $F$-regularity, Mém. Soc. Math. France (N.S.) 38 (1989), 119–133. Colloque en l’honneur de Pierre Samuel (Orsay, 1987). MR 1044348
Melvin Hochster and Joel L. Roberts, The purity of the Frobenius and local cohomology, Advances in Math. 21 (1976), no. 2, 117–172. MR 417172, DOI 10.1016/0001-8708(76)90073-6
Ernst Kunz, Characterizations of regular local rings of characteristic $p$, Amer. J. Math. 91 (1969), 772–784. MR 252389, DOI 10.2307/2373351
Ernst Kunz, On Noetherian rings of characteristic $p$, Amer. J. Math. 98 (1976), no. 4, 999–1013. MR 432625, DOI 10.2307/2374038
K. E. Smith, F-rational rings have rational singularities, preprint.
Keiichi Watanabe, $F$-regular and $F$-pure normal graded rings, J. Pure Appl. Algebra 71 (1991), no. 2-3, 341–350. MR 1117644, DOI 10.1016/0022-4049(91)90157-W