Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Strong F-regularity in images of regular rings

Author: Donna Glassbrenner
Journal: Proc. Amer. Math. Soc. 124 (1996), 345-353
MSC (1991): Primary 13A35
MathSciNet review: 1291770
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • Fe R. Fedder, F-purity and rational singularity, Trans. Amer. Math. Soc. 278 (1983), 461--480, MR 84h:13031.
  • FW R. Fedder and K. Watanabe, A characterization of F-regularity in terms of F-purity, Math. Sci. Res. Inst. Publ., no. 15, Springer-Verlag, New York, 1989, pp. (227--245), MR 91k:13009.
  • Ha N. Hara, F-regularity and F-purity of graded rings, J. Algebra (to appear).
  • Ho 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.
  • HH1 M. Hochster and C. Huneke, Tight closure, invariant theory and Briançon-Skoda theorem, J. Amer. Math. Soc. 3 (1990), 31--116, MR 91g:13010.
  • HH2 ------, Tight closures of parameter ideals and splitting in module-finite extensions, preprint.
  • HH3 ------, F-regularity, test elements, and smooth base change, preprint.
  • HH4 ------, Tight closure and strong F-regularity, Soc. Math. France, Paris, 1989, pp. (119--133), MR 91i:13025.
  • HR M. Hochster and J. L. Roberts, The purity of the Frobenius and local cohomology, Adv. Math. 21 (1976), 117--172, MR 54:5230.
  • Ku1 E. Kunz, Characterizations of regular local rings of characteristic $p$, Amer. J. Math. 91 (1969), 772--784, MR 40:5609.
  • Ku2 ------, On Noetherian rings of characteristic $p$, Amer. J. Math. 98 (1976), 999--1013, MR 55:5612.
  • S K. E. Smith, F-rational rings have rational singularities, preprint.
  • Wa K. Watanabe, F-regular and F-pure normal graded rings, J. Pure Appl. Algebra 71 (1991), 341--350, MR 92g:13003.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 13A35

Retrieve articles in all journals with MSC (1991): 13A35

Additional Information

Donna Glassbrenner
Affiliation: Department of Mathematics, University of Virginia, Charlottesville, Virginia 22903

Keywords: Tight closure, strong F-regularity
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 1996 American Mathematical Society