Commutative Algebra pp 305-324
- 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
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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