Tight Closure

  • Melvin Hochster
  • Craig Huneke
Conference paper

DOI: 10.1007/978-1-4612-3660-3_15

Part of the Mathematical Sciences Research Institute Publications book series (MSRI, volume 15)
Cite this paper as:
Hochster M., Huneke C. (1989) Tight Closure. In: Hochster M., Huneke C., Sally J.D. (eds) Commutative Algebra. Mathematical Sciences Research Institute Publications, vol 15. Springer, New York, NY

Abstract

Throughout this paper all rings are commutative, with identity, and Noetherian, unless otherwise specified. We will summarize many of the results in [H-H] concerning the theory of tight closure and prove several basic theorems using this theory in characteristic p, including the theorem of Briançon-Skoda that the integral closure of the nth power of an n-generator ideal of a regular ring is contained in the ideal, the monomial conjecture, the syzygy theorem, and that summands of regular rings are Cohen-Macaulay (C-M).

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Copyright information

© Springer-Verlag New York Inc. 1989

Authors and Affiliations

  • Melvin Hochster
    • 1
    • 2
  • Craig Huneke
    • 1
    • 2
  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA
  2. 2.Department of MathematicsPurdue UniversityWest LafayetteUSA

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