Strong F-regularity in images of regular rings

Author:
Donna Glassbrenner

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

MSC (1991):
Primary 13A35

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

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.

**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*, Amer. J. Math.**91**(1969), 772--784, MR**40:5609**.**Ku2**------,*On Noetherian rings of characteristic*, 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**.

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

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

Keywords:
Tight closure,
strong F-regularity

Communicated by:
Wolmer V. Vasconcelos

Article copyright:
© Copyright 1996
American Mathematical Society