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Tight closure in F-rational rings

Published online by Cambridge University Press:  22 January 2016

Ian M. Aberbach
Ian M. Aberbach*
Affiliation:
Department of Mathematics, University of Missouri, Columbia, MO 65211, U. S. A.
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All rings are commutative with unit and modules are unital. With one exception all rings are Noetherian. We consider only rings of positive characteristic p. Section 0 contains background, definitions and terminology.

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 135 , September 1994 , pp. 43 - 54
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1994

References

[A] Aberbach, I. M., Finite phantom projective dimension, Amer. J. Math., 116 (1994), 447–477.Google Scholar
[AHH] Aberbach, I. M., Hochster, M. and Huneke, C., Localization of tight closure and modules of finite phantom projective dimension, J. reine angew. Math., 434 (1993), 67–114.Google Scholar
[BE] Buchsbaum, D. A. and Eisenbud, D., What Makes a Complex Exact?, J. Algebra, 25 (1973), 259–268.Google Scholar
[CE] Cartan, H. and Eilenberg, S., Homological Algebra, Princeton University Press, Princeton, 1956.Google Scholar
[FW] Fedder, R. and Watanabe, K., A characterization of F-regularity in terms of F-purity, Commutative Algebra (Proceedings of a Microprogram held June 15-July 2, 1987), Mathematical Sciences Research Institute Publications, vol. 15, Springer-Verlag, New York-Berlin-Heidelberg-London-Paris-Tokyo, 1989, pp. 227–245.Google Scholar
[H] Hochster, M., Topics in the homological theory of modules over commutative rings, C.B.M.S. Regional Conf. Ser. in Math. no. 24, Amer. Math. Soc, Providence, R. I., 1975.Google Scholar
[HH1] Hochster, M. and Huneke, C., Tight closure, invariant theory, and the Briançon-Skoda theorem, J. Amer. Soc, 3 (1990), 31–116.Google Scholar
[HH2] Hochster, M. and Huneke, C., Infinite integral extensions and big Cohen-Macaulay algebras, Annals of Math., 135 (1992), 53–89.Google Scholar
[HH3] Hochster, M. and Huneke, C., F-regularity, test elements, and smooth base change, preprint.Google Scholar
[HH4] Hochster, M. and Huneke, C., Phantom homology, Memoirs of the Amer. Math. Soc, Providence, R. I., 1993.Google Scholar
[PS] Peskine, C. and Szpiro, L., Dimension projective finie et cohomologie locale, I.H.E.S. Publ. Math., 42 (1973), 323–395.Google Scholar
[S] Smith, K. E., Tight closure of parameter ideals, Invent. Math., 115 (1994), 41–60.Google Scholar