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Big and small Cohen-Macaulay modules

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References

  1. M. Artin, On the solutions of analytic equations, Invent. Math. 5 (1968), 277–291.

    Article  MathSciNet  MATH  Google Scholar 

  2. M. Artin, Algebraic approximation of structures over complete local rings, Publ. Math. I.H.E.S., Paris, No. 36, 1969.

    Google Scholar 

  3. M. Auslander, Modules over unramified regular local rings, Illinois J. of Math. 5 (1961), 631–645.

    MathSciNet  MATH  Google Scholar 

  4. M. Auslander, Modules over unramified regular local rings, Proc. Intern. Congress of Math., 1962, 230–233.

    Google Scholar 

  5. M. Auslander and D. A. Buchsbaum, Homological dimension in Noetherian rings, Proc. Nat. Acad. Sci. USA 42 (1956), 36–38.

    Article  MathSciNet  MATH  Google Scholar 

  6. M. Auslander and D. A. Buchsbaum, Homological dimension in local rings, Trans. Amer. Math. Soc. 85 (1957), 390–405.

    Article  MathSciNet  MATH  Google Scholar 

  7. M. Auslander and D. A. Buchsbaum, Codimension and multiplicity, Ann. of Math. 68 (1958), 625–657; corrections, Ann. of Math. 70 (1959), 395–397.

    Article  MathSciNet  MATH  Google Scholar 

  8. H. Bass, On the ubiquity of Gorenstein rings, Math. Z. 82 (1963), 8–28.

    Article  MathSciNet  MATH  Google Scholar 

  9. D. Eisenbud, Some directions of recent progress in commutative algebra, Proc. of Symposium in Pure Math. 29, Amer. Math. Soc., 1975, 111–128.

    Article  MathSciNet  MATH  Google Scholar 

  10. D. Eisenbud and E. G. Evans, A generalized principal ideal theorem, Nagoya Math. J. 62 (1976), 41–53.

    Article  MathSciNet  MATH  Google Scholar 

  11. D. Ferrand and M. Raynaud, Fibres formelles d'un anneau local noethérien, Ann. Sci. Ec. Norm. Sup. (4) 3 (1970), 295–311.

    MathSciNet  MATH  Google Scholar 

  12. R. Fossum, H.-B. Foxby, P. Griffith, and I. Reiten, Minimal injective resolutions with applications to dualizing modules and Gorenstein modules, Publ. Math. I.H.E.S. Paris No. 45, 1975, 193–215.

    Google Scholar 

  13. H.-B. Foxby, On the μi in a minimal injective resolution, Math. Scand. 29 (1971), 175–186.

    MathSciNet  Google Scholar 

  14. H.-B. Foxby, Applications of isomorphisms between complexes, preprint (Copenhagen University).

    Google Scholar 

  15. H.-B. Foxby, On the μi in a minimal injective resolution II, Copenhagen Math. Inst. preprint series, Aug. 1976, No. 20.

    Google Scholar 

  16. P. Griffith, A representation theorem for complete local rings, J. Pure and Applied Algebra 7 (1976), 303–315.

    Article  MathSciNet  MATH  Google Scholar 

  17. A. Grothendieck (notes by R. Hartshorne), "Local Cohomology", Lecture Notes in Math. no. 41, Springer, New York, 1967.

    MATH  Google Scholar 

  18. M. Hochster, Cohen-Macaulay modules, Proc. Kansas Commutative Algebra Conference, Springer-Verlag Lecture Notes in Math., No. 311, New York, 1973 120–152.

    Google Scholar 

  19. M. Hochster, Contracted ideals from integral extensions of regular rings, Nagoya Math. J. 51 (1973), 25–43.

    Article  MathSciNet  MATH  Google Scholar 

  20. M. Hochster, Deep local rings, preliminary preprint, Århus University preprint series, December, 1973.

    Google Scholar 

  21. M. Hochster, The equicharacteristic case of some homological conjectures on local rings, Bull. Amer. Math. Soc. 80 (1974), 683–686.

    Article  MathSciNet  MATH  Google Scholar 

  22. M. Hochster, "Topics in the homological theory of modules over commutative rings", C.B.M.S. Regional Conference Series in Math. No. 24, Amer. Math. Soc., Providence, 1975.

    Google Scholar 

  23. M. Hochster, Big Cohen-Macaulay modules and algebras and embeddability in rings of Witt vectors, "Proc. of the Queen's University Commutative Algebra Conference" (Kingston, Ontario, Canada, 1975) Queen's Papers in Pure and Applied Math. No. 42, 106–195.

    Google Scholar 

  24. M. Hochster, Some applications of the Frobenius in characteristic zero, Bull. Amer. Math. Soc., to appear.

    Google Scholar 

  25. M. Hochster, The canonical element conjecture, in preparation.

    Google Scholar 

  26. B. Iversen, Amplitude inequalities for complexes, Aarhus University Preprint Series No. 36 (1976/77).

    Google Scholar 

  27. I. Kaplansky, "Commutative Rings", Allyn and Bacon, Boston, 1970. Revised ed., 1974.

    MATH  Google Scholar 

  28. G. Levin and W. Vasconcelos, Homological dimensions and Macaulay rings, Pacific J. Math. 25 (1968), 315–328.

    Article  MathSciNet  MATH  Google Scholar 

  29. H. Matsumura, "Commutative algebra", Benjamin, New York, 1970.

    MATH  Google Scholar 

  30. M. Nagata, "Local rings", Interscience, New York, 1962.

    MATH  Google Scholar 

  31. C. Peskine and L. Szpiro, Notes sur un air de H. Bass, unpublished preprint (Brandeis University, Waltham, Massachusetts).

    Google Scholar 

  32. C. Peskine and L. Szpiro, Dimension projective finie et cohomologie locale, Publ. Math. I.H.E.S., Paris, No. 42, 1973, 323–395.

    Google Scholar 

  33. C. Peskine and L. Szpiro, Syzgies et multiplicités, C. R. Acad. Sci., Paris, Ser. A. (1974), 1421–1424.

    Google Scholar 

  34. M. Raynaud, "Anneaux locaux henséliens", Springer-Verlag Lecture Notes in Math. No. 169, New York, 1970.

    Google Scholar 

  35. D. Rees, The grade of an ideal or module, Proc. Cambridge Philos. Soc. 53 (1957), 28–42.

    Article  MathSciNet  MATH  Google Scholar 

  36. P. Roberts, Two applications of dualizing complexes over local rings, Ann. Scient. Ec. Norm. Sup. (4) 9 (1976), 103–106.

    MathSciNet  MATH  Google Scholar 

  37. J.-P. Serre, Sur la dimension homologique des anneaux et des modules Noethériens, Proc. Internat. Sympos. Algebraic Number Theory, Tokyo, 1955, 175–189.

    Google Scholar 

  38. J.-P. Serre, Algèbre locale. Multiplicités. Springer-Verlag Lecture Notes in Math. No. 11, New York, 1965.

    Google Scholar 

  39. O. Zariski and P. Samuel, "Commutative algebra", Vol. 1, Princeton, Van Nostrand, 1958.

    MATH  Google Scholar 

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Carl Faith Sylvia Wiegand

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© 1979 Springer-Verlag

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Hochster, M. (1979). Big and small Cohen-Macaulay modules. In: Faith, C., Wiegand, S. (eds) Module Theory. Lecture Notes in Mathematics, vol 700. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0063464

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  • DOI: https://doi.org/10.1007/BFb0063464

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  • Print ISBN: 978-3-540-09107-3

  • Online ISBN: 978-3-540-35538-0

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