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Symmetric algebras

  • Wolmer V. Vasconcelos
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1430)

Keywords

Exact Sequence Prime Ideal Complete Intersection Integral Domain Polynomial Ring 
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References

  1. [1]
    M. Auslander, Modules over unramified regular local rings, Illinois J. Math. 5 (1961), 631–647.MathSciNetzbMATHGoogle Scholar
  2. [2]
    M. Auslander and O. Goldman, Maximal orders, Trans. Amer. Math. Soc. 97 (1960), 1–24.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    L. Avramov, Complete intersections and symmetric algebras, J. Algebra 73 (1980), 249–280.MathSciNetGoogle Scholar
  4. [4]
    J. Barshay, Graded algebras of powers of ideals generated by A-sequences, J. Algebra 25 (1973), 90–99.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    D. Bayer and M. Stillman, Macaulay, A computer algebra system for computing in algebraic geometry and commutative algebra, 1988.Google Scholar
  6. [6]
    J. Brennan, M. Vaz Pinto and W. V. Vasconcelos, The Jacobian module of a Lie algebra, Trans. Amer. Math. Soc., to appear.Google Scholar
  7. [7]
    W. Bruns, Additions to the theory of algebras with straightening law, in Commutative Algebra (M. Hochster, C. Huneke and J.D. Sally, Eds.), MSRI Publications 15, Springer-Verlag, New York, 1989, 111–138.CrossRefGoogle Scholar
  8. [8]
    D. Buchsbaum and D. Eisenbud, What makes a complex exact?, J. Algebra 25 (1973), 259–268.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    D. Costa, L. Gallardo and J. Querré, On the distribution of prime elements in polynomial Krull domains, Proc. Amer. Math. Soc. 87 (1983), 41–43.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    D.L. Costa and J.L. Johnson, Inert extensions for Krull domains, Proc. Amer. Math. Soc. 59 (1976), 189–194.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    J. Eagon and D. G. Northcott, Ideals defined by matrices and a certain complex associated with them, Proc. Royal Soc. 269 (1962), 188–204.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    E. G. Evans and P. Griffith, The syzygy problem, Annals of Math. 114 (1981), 323–333.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    H. fitting, Die Determinantenideale Moduls, Jahresbericht DMV 46 (1936), 192–228.zbMATHGoogle Scholar
  14. [14]
    O. Forster, Über die Anzahl der Erzeugenden eines Ideals in einem Noetherschen Ring, Math. Z. 84 (1964), 80–87.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    F. R. Gantmacher, Applications of the Theory of Matrices, Interscience, New York, 1959.zbMATHGoogle Scholar
  16. [16]
    M. Gerstenhaber, On dominance and varieties of commuting matrices, Annals of Math. 73 (1961), 324–348.MathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    R. Gilmer, Multiplicative Ideal Theory, M. Dekker, New York, 1972.zbMATHGoogle Scholar
  18. [18]
    J. Herzog, Certain complexes associated to a sequence and a matrix, Manuscripta Math. 12 (1974), 217–247.MathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    J. Herzog, A. Simis and W. V. Vasconcelos, Approximation complexes of blowing-up rings, J. Algebra 74 (1982), 466–493.MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    J. Herzog, A. Simis and W. V. Vasconcelos, Koszul homology and blowing-up rings, Proc. Trento Commutative Algebra Conf., Lectures Notes in Pure and Applied Math., vol. 84, Dekker, New York, 1983, 79–169.Google Scholar
  21. [21]
    J. Herzog, A. Simis and W. V. Vasconcelos, On the arithmetic and homology of algebras of linear type, Trans. Amer. Math. Soc. 283 (1984), 661–683.MathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    J. Herzog, A. Simis and W. V. Vasconcelos, Arithmetic of normal Rees algebras, Preprint, 1988.Google Scholar
  23. [23]
    J. Herzog, W. V. Vasconcelos and R. Villarreal, Ideals with sliding depth, Nagoya Math. J. 99 (1985), 159–172.MathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    M. Hochster, The Zariski-Lipman conjecture in the graded case, J. Algebra 47 (1977), 411–424.MathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    J. E. Humphreys, Introduction to Lie Algebras and Representation Theory, Springer-Verlag, Berlin, 1972.CrossRefzbMATHGoogle Scholar
  26. [26]
    C. Huneke, On the symmetric algebra of a module, J. Algebra 69 (1981), 113–119.MathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    C. Huneke, Determinantal ideals of linear type, Arch. Math. 47 (1986), 324–329.MathSciNetCrossRefzbMATHGoogle Scholar
  28. [28]
    C. Huneke, On the symmetric and Rees algebras of an ideal generated by a d-sequence, J. Algebra 62 (1980), 268–275.MathSciNetCrossRefzbMATHGoogle Scholar
  29. [29]
    C. Huneke, Linkage and Koszul homology of ideals, Amer. J. Math. 104 (1982), 1043–1062.MathSciNetCrossRefzbMATHGoogle Scholar
  30. [30]
    C. Huneke, Strongly Cohen-Macaulay schemes and residual intersections, Trans. Amer. Math. Soc. 277 (1983), 739–763.MathSciNetCrossRefzbMATHGoogle Scholar
  31. [31]
    C. Huneke and M. E. Rossi, The dimension and components of symmetric algebras, J. Algebra 98 (1986), 200–210.MathSciNetCrossRefzbMATHGoogle Scholar
  32. [32]
    C. Huneke and B. Ulrich, Residual intersections, J. reine angew. Math. 390 (1988), 1–20.MathSciNetzbMATHGoogle Scholar
  33. [33]
    T. Jòsefiak, Ideals generated by the minors of a symmetric matrix, Comment. Math. Helvetici 53 (1978), 595–607.MathSciNetCrossRefGoogle Scholar
  34. [34]
    B. Kostant, Lie group representations on polynomial rings, Amer. J. Math. 85 (1963), 327–404.MathSciNetCrossRefzbMATHGoogle Scholar
  35. [35]
    B. V. Kotsev, Determinantal ideals of linear type of a generic symmetric matrix, J. Algebra, to appear.Google Scholar
  36. [36]
    L. Lebelt, Freie Auflösungen äußerer Potenzen, Manuscripta Math. 21 (1977), 341–355.MathSciNetCrossRefzbMATHGoogle Scholar
  37. [37]
    S. Lichtenbaum, On the vanishing of Tor in regular local rings, Illinois J. Math. 10 (1966), 220–226.MathSciNetzbMATHGoogle Scholar
  38. [38]
    J. Lipman, Free derivation modules on algebraic varieties, American J. Math. 87 (1965), 874–898.MathSciNetCrossRefzbMATHGoogle Scholar
  39. [39]
    R. MacRae, On an application of the Fitting invariants, J. Algebra 2 (1965), 153–169.MathSciNetCrossRefzbMATHGoogle Scholar
  40. [40]
    H. Matsumura, Commutative Algebra, Benjamin/Cummings, Reading, Massachusetts, 1980.zbMATHGoogle Scholar
  41. [41]
    A. Micali, Sur les algèbres universalles, Annales Inst. Fourier 14 (1964), 33–88.MathSciNetCrossRefzbMATHGoogle Scholar
  42. [42]
    A. Micali, P. Salmon and P. Samuel, Integrité et factorialité des algèbres symétriques, Atas do IV Colóquio Brasileiro de Matemática, SBM, (1965), 61–76.Google Scholar
  43. [43]
    T. Motzkin and O. Taussky, Pairs of matrices with property L II, Trans. Amer. Math. Soc. 80 (1955), 387–401.MathSciNetzbMATHGoogle Scholar
  44. [44]
    M. Nagata, Local Rings, Interscience, New York, 1962.zbMATHGoogle Scholar
  45. [45]
    R. W. Richardson, Commuting varieties of semisimple Lie algebras and algebraic groups, Compositio Math. 38 (1979), 311–327.MathSciNetzbMATHGoogle Scholar
  46. [46]
    P. Roberts, A prime ideal in a polynomial ring whose symbolic blow-up is not Noetherian, Proc. Amer. Math. Soc. 94 (1985), 589–592.MathSciNetCrossRefzbMATHGoogle Scholar
  47. [47]
    P. Roberts, An infinitely generated symbolic blow-up in a power series ring and a new counterexample to Hilbert's Fourteenth Problem, J. Algebra, to appear.Google Scholar
  48. [48]
    P. Samuel, Anneaux gradués factoriels et modules réflexifs, Bull. Soc. Math. France 92 (1964), 237–249.MathSciNetzbMATHGoogle Scholar
  49. [49]
    A. Simis, Selected Topics in Commutative Algebra, Lecture Notes, IX Escuela Latinoamericana de Matematica, Santiago, Chile, 1988.Google Scholar
  50. [50]
    A. Simis and W. V. Vasconcelos, The syzygies of the conormal module, Amer. J. Math. 103 (1981), 203–224.MathSciNetCrossRefzbMATHGoogle Scholar
  51. [51]
    A. Simis and W. V. Vasconcelos, On the dimension and integrality of symmetric algebras, Math. Z. 177 (1981), 341–358.MathSciNetCrossRefzbMATHGoogle Scholar
  52. [52]
    A. Simis and W. V. Vasconcelos, The Krull dimension and integrality of symmetric algebras, Manuscripta Math. 61 (1988), 63–78.MathSciNetCrossRefzbMATHGoogle Scholar
  53. [53]
    G. Valla, On the symmetric and Rees algebras of an ideal, Manuscripta Math. 30 (1980), 239–255.MathSciNetCrossRefzbMATHGoogle Scholar
  54. [54]
    W. V. Vasconcelos, On linear complete intersections, J. Algebra 111 (1987), 306–315.MathSciNetCrossRefzbMATHGoogle Scholar
  55. [55]
    W. V. Vasconcelos, Symmetric algebras and factoriality, in Commutative Algebra (M. Hochster, C. Huneke and J. D. Sally, Eds.), MSRI Publications 15, Springer-Verlag, New York, 1989, 467–496.CrossRefGoogle Scholar
  56. [56]
    W. V. Vasconcelos, The complete intersection locus of certain ideals, J. Pure and Applied Algebra 38 (1985), 367–378.MathSciNetCrossRefzbMATHGoogle Scholar
  57. [57]
    W. V. Vasconcelos, On the structure of certain ideal transforms, Math. Z. 198 (1988), 435–448.MathSciNetCrossRefzbMATHGoogle Scholar
  58. [58]
    W. V. Vasconcelos, Modules of differentials of symmetric algebras, Arch. Math., to appear.Google Scholar
  59. [59]
    U. Vetter, Zu einem Satz von G. Trautmann über den Rang gewisser kohärenter analytischer Moduln, Arch. Math. 24 (1973), 158–161.MathSciNetCrossRefzbMATHGoogle Scholar
  60. [60]
    R. Villarreal, Rees algebras and Koszul homology, J. Algebra 119 (1988), 83–104.MathSciNetCrossRefzbMATHGoogle Scholar
  61. [61]
    R. Villarreal, Cohen-Macaulay graphs, Preprint, 1988.Google Scholar
  62. [62]
    J. Weyman, Resolutions of the exterior and symmetric powers of a module, J. Algebra 58 (1979), 333–341.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Wolmer V. Vasconcelos
    • 1
  1. 1.Department of MathematicsRutgers UniversityNew BrunswickUSA

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