Skip to main content
SpringerLink
Log in

Relative invariants for commutative rings

  • Conference paper
  • First Online:
Séminaire d’Algèbre Paul Dubreil et Marie-Paule Malliavin

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1029))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Auslander B., The Brauer group of a ringed space, J. Algebra 4 (1966) 220–273.

    Article  MathSciNet  MATH  Google Scholar 

  2. Auslander B., Central separable algebras which are locally endomorphism rings of free modules, Proc. A.M.S. 30 (1971) 395–404.

    Article  MathSciNet  MATH  Google Scholar 

  3. Auslander M., Goldman O., The Brauer group of a commutative ring, Trans. A.M.S. 97 (1960) 367–409.

    Article  MathSciNet  MATH  Google Scholar 

  4. Auslander M., Goldman O., Maximal orders, Trans. A.M.S. 97 (1960) 1–24.

    Article  MathSciNet  MATH  Google Scholar 

  5. Bass H., Algebraic K-theory, Benjamin, New-York 1968

    MATH  Google Scholar 

  6. Bourbaki N., Algèbre commutative, Eléments de Math. 27, 28, 30, 31, Hermann, Paris, 1961–66.

    Google Scholar 

  7. De Meyer F., Ingraham E., Separable Algebras over Commutative Rings, LNM 181, Springer Verlag, Berlin 1971.

    MATH  Google Scholar 

  8. Fossum R., The Divisor Class Group of a Krull Domain, Ergebnisse der Math. 74, Springer Verlag, Berlin 1973.

    Book  MATH  Google Scholar 

  9. Gabber O., Some theorems on Azumaya Algebras, in: Groupe de Brauer, LNM 844, Springer Verlag, Berlin 1981, 129–209.

    Chapter  Google Scholar 

  10. Gabriel P, Des catégories abeliennes, Bull. Soc. Math. France 90, (1962) 323–448.

    MathSciNet  MATH  Google Scholar 

  11. Gabriel P, Popescu N, Caractérisation des catégories abéliennes avec générateurs et limites inductives exactes, C.R. Ac. Sci. Paris, 258 (1964) 4188–4190.

    MATH  Google Scholar 

  12. Golan J. Localization in Noncommutative rings, Pure and Appl. Math., M. Dekker, New York 1975.

    Google Scholar 

  13. Goldman O, Rings and Modules of Quotients, J. Of algebra 13 (1969) 10–47.

    Article  MathSciNet  MATH  Google Scholar 

  14. Grothendieck A. Le groupe de Brauer, I, II, III, in: "Dix exposés sur la Cohomologie des Schémas", North Holland, Amsterdam.

    Google Scholar 

  15. Hartshorne R., Algebraic Geometry, Springer Verlag, Berlin 1977.

    Book  MATH  Google Scholar 

  16. Ischebeck F. Zur Picard Gruppe eines Produktes, Math. Z. 139,(1974) 141–157.

    Article  MathSciNet  MATH  Google Scholar 

  17. Nastasescu C., Van Oystaeyen F., Graded and filtered Rings and Modules, LNM 758, Springer Verlag, Berlin 1979.

    MATH  Google Scholar 

  18. Orzech M., Brauer Groups and Class Groups for a Krull Domain, in: "Brauer Groups in Ring Theory and Algebraic Geometry", LNM 917, Springer Verlag, Berlin 1982.

    Google Scholar 

  19. Orzech M., Small C., The Brauer Group of a commutative Ring, Marcel Dekker, New-York 1975.

    MATH  Google Scholar 

  20. Orzech M., Verschoren A., Some Remarks on Brauer Groups of Krull Domains, LNM 917, Springer Verlag, Berlin 1982.

    MATH  Google Scholar 

  21. Stenström B., Rings of Quotients, Springer Verlag, Berlin 1975.

    Book  MATH  Google Scholar 

  22. Van Oystaeyen F., On graded Rings and Modules of Quotients, Comm. in algebra 6 (1978) 1923–1959.

    Article  MathSciNet  MATH  Google Scholar 

  23. Van Oystaeyen F. Prime Spectra in Non-commutative Algebra, LNM 444, Springer Verlag, Berlin, 1975.

    Book  MATH  Google Scholar 

  24. Van Oystaeyen F., Graded Azumaya Algebras and Brauer Groups, in: "Proceedings Ring Theory, U.I.A., 1980", LNM 825, Springer Verlag, Berlin 1980.

    Chapter  Google Scholar 

  25. Van Oystaeyen F., Verschoren A., Reflectors and localization. Application to sheaf theory, M. Dekker, New-York 1979.

    MATH  Google Scholar 

  26. Van Oystaeyen F. Verschoren A., The Brauer Group of a Projective Variety, Israël J. Math. 42 (1982) 37–59.

    Article  MathSciNet  MATH  Google Scholar 

  27. Van Oystaeyen F. Verschoren A., The Brauer Group of a Projective Curve, Israël J. Math, 42 (1982) 327–333.

    Article  MathSciNet  MATH  Google Scholar 

  28. Van Oystaeyen F. Verschoren A., Relative Invariants of Rings, Part I: The Commutative Theory, Marcel Dekker, New-York 1983.

    MATH  Google Scholar 

  29. Verschoren A, On the Picard Group of a Grothendieck Category, Comm. Algebra 8 (1980) 1169–1194.

    Article  MathSciNet  MATH  Google Scholar 

  30. Verschoren A., The Brauer group of a quasi-affine scheme, in: "Brauer groups in Ring theory and Algebraic Geometry, LNM 917, Springer Verlag, Berlin 260–278.

    Google Scholar 

  31. Verschoren A., On the reflexive class group, Indag. Math., to appear.

    Google Scholar 

  32. Verschoren A., Exact sequences for relative Brauer groups and Picard groups, J. Pure and Appl. Algebra, to appear.

    Google Scholar 

  33. Verschoren A., On the Picard group of a quasi-affine scheme, to appear.

    Google Scholar 

  34. Yuan S., Reflexive Modules and Algebra Class Groups over Noetherian Integrally closed Domains, I. of Algebra 32 (1974) 405–417.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Antwerp, U. I. A., Belgium

    A. Verschoren

Authors
  1. A. Verschoren
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Marie-Paule Malliavin

Rights and permissions

Reprints and permissions

Copyright information

© 1983 Springer-Verlag

About this paper

Cite this paper

Verschoren, A. (1983). Relative invariants for commutative rings. In: Malliavin, MP. (eds) Séminaire d’Algèbre Paul Dubreil et Marie-Paule Malliavin. Lecture Notes in Mathematics, vol 1029. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0098934

Download citation

  • DOI: https://doi.org/10.1007/BFb0098934

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12699-7

  • Online ISBN: 978-3-540-38686-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation