Advertisement

Brauer groups and class groups for a Krull domain

  • Morris Orzech
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 917)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    B. Auslander, The Brauer group of a ringed space, J. of Algebra 4 (1966), 220–273.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    -, Central separable algebras which are locally endomorphism rings of free modules, Proc. Amer. Math. Soc. 30 (1971), 395–404.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    M. Auslander and O. Goldman, The Brauer group of a commutative ring, Trans. Amer. Math. Soc. 97 (1960), 367–409.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    H. Bass, Algebraic K-Theory, W.A. Benjamin, Inc., New York, 1968.zbMATHGoogle Scholar
  5. [5]
    N. Bourbaki, Algébre Commutative, Hermann, Paris, 1965.zbMATHGoogle Scholar
  6. [6]
    L.N. Childs, On Brauer groups of some normal local rings, Brauer Groups, Evanston 1975, Lecture Notes in Mathematics No. 549, Springer-Verlag, Berlin, 1976, 1–13.Google Scholar
  7. [7]
    L.N. Childs, G. Garfinkel and M. Orzech, On the Brauer group and factoriality of normal domains, J. Pure and Appl. Algebra 6 (1975), 111–123.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    S.B. Conlon, An extension of the Krull-Schmidt theorem, Bull. Austral. Math. Soc. 1 (1969), 109–114.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    F. DeMeyer, The Brauer group of polynomial rings, Pacific J. Math. 59 (1975), 391–398.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    E.G. Evans, Jr., Krull-Schmidt and cancellation over local rings, Pacific J. Math. 46 (1973), 115–121.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    R.M. Fossum, The Divisor Class Group of a Krull Domain, Ergebnisse der Mathematik 74, Springer-Verlag, New York, 1973.CrossRefzbMATHGoogle Scholar
  12. [12]
    G. Garfinkel, Amitsur cohomology and an exact sequence involving Pic and the Brauer group, Ph., thesis, Cornell Univ., 1968.Google Scholar
  13. [13]
    G. Garfinkel, A torsion version of the Chase-Rosenberg exact sequence, Duke Math. J. 42 (1975), 195–210.MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    P.A. Griffith, The Brauer group of A[T], Math. Zeit. 147 (1976), 79–86.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    A. Grothendieck, Le groupe de Brauer, I. Dix Exposés sur la Cohmologie des Schemas, North-Holland Pub. Co. 1968, 46–65.Google Scholar
  16. [16]
    R.T. Hoobler, A generalization of the Brauer group and Amitsur cohomology, Ph.D. thesis, University of California, Berkeley, 1966.Google Scholar
  17. [17]
    H. Lee and M. Orzech, Brauer groups of a Krull scheme, Queen's Papers in Pure & Applied Mathematics, to appear.Google Scholar
  18. [18]
    M. Orzech, Divisorial modules and Krull morphisms, Queen's Mathematics Preprint, 1981-12.Google Scholar
  19. [19]
    D. Saltman, Azumaya algebras with involution. J. Algebra 52 (1978), 526–539.MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    S. Yuan, Reflexive modules and algebra class groups over noetherian integrally closed domains, J. of Algebra 32 (1974), 405–417.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Morris Orzech
    • 1
  1. 1.Queen's UniversityKingstonCanada

Personalised recommendations