Skip to main content
Log in

The Bass-Murthy question: Serre dimension of Laurent polynomial extensions

  • Published:
Inventiones mathematicae Aims and scope

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  • [B] Bass, H.: Libération des modules projectifs sur certains anneaux de polynomes. Semin. Bourbaki488, no. 448 (1973/74). In: Lect. Notes Math.431, 228–254. Berlin-Heidelberg-New York: Springer 1975

    Google Scholar 

  • [BM] Bass, H., Murthy, M.P.: Grothendieck groups and Picard groups of abelian group rings. Ann. Math.86, 16–73 (1967)

    Google Scholar 

  • [BR-1] Bhatwadekar, S.M., Roy, A.: Stability theorem for overrings of polynomial rings. Invent. Math.68, 117–127 (1982)

    Google Scholar 

  • [BR-2] Bhatwadekar, S.M., Roy, A.: Some theorems about projective modules over polynomial rings. J. Algebra86, 150–158 (1983)

    Google Scholar 

  • [BR-3] Bhatwadekar, S.M., Roy, A.: Inversion of monic polynomials and the existence of unimodular elements. Math. Z.183, 87–94 (1983)

    Google Scholar 

  • [EE] Eisenbud, D., Evans, G.: Generating modules efficiently—theorems from AlgebraicK-Theory. J. Algebra27, 278–305 (1973)

    Google Scholar 

  • [G] Gabel, M.R.: Generation and projective generation of ideals. J. Algebra76, 186–191 (1982)

    Google Scholar 

  • [Kg] Kang, M.-C.: Projective modules over some polynomial rings. J. Algebra59, 65–76 (1979)

    Google Scholar 

  • [Ka] Karoubi, M.: Localisations de formes quadratiques I. Ann. Sci. ENS7, 359–404 (1974)

    Google Scholar 

  • [L] Lindel, H.: On projective modules over positively graded rings. (To appear in Proc. Int. Coll. on “Vector Bundles on Projective and Affine Varieties”.) Tata Institute, Bombay (1984)

    Google Scholar 

  • [Mn] Mandal, S.: On efficient generation of ideals. Invent. Math.75, 59–67 (1984)

    Google Scholar 

  • [Mu] Murthy, M.P.: Lectures on Projective Modules. Notes by J. Yanik

  • [P] Plumstead, B.R.: The Conjectures of Eisenbud and Evans. Am. J. Math.105, 1417–1433 (1983)

    Google Scholar 

  • [Q] Quillen, D.: Projective modules over polynomial rings. Invent. Math.36, 167–171 (1976)

    Google Scholar 

  • [Ra] Rao, R.A.: Stability theorems for overrings of polynomial rings II. J. Algebra78, 437–444 (1982)

    Google Scholar 

  • [Ry] Roy, A.: Applications of patching diagrams to some questions about projective modules. J. Pure Appl. Algebra24, 313–319 (1982)

    Google Scholar 

  • [Su] Suslin, A.A.: On the structure of the special linear group over polynomial rings. Math. USSR, Izwestija11, 221–238 (1977)

    Google Scholar 

  • [Sw] Swan, R.G.: Projective modules over Laurent polynomial rings. Trans. Am. Soc.237, 111–120 (1978)

    Google Scholar 

  • [Vo] Vorst, A.C.F.: The General Linear Group of Polynomial Rings over Regular Rings. Commun. Algebra9, 425–451 (1981)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bhatwadekar, S.M., Lindel, H. & Rao, R.A. The Bass-Murthy question: Serre dimension of Laurent polynomial extensions. Invent Math 81, 189–203 (1985). https://doi.org/10.1007/BF01388777

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01388777

Keywords

Navigation