Skip to main content

Generating modules efficiently over noncommutative 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 924))

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.00
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

  • [B] H. Bass, K-theory and stable structure, Publ. Math. I.H.E.S. 22 (1964), 5–60.

    Article  MathSciNet  Google Scholar 

  • [EE] D. Eisenbud and E.G. Evans, Jr., Generating modules efficiently: theorems from algebraic K-theory, J. Algebra 27 (1973), 278–305.

    Article  MathSciNet  MATH  Google Scholar 

  • [FH] F.T. Farrell and W.C. Hsiang, A formula for K1Rα[t], Proc. Symp. Pure Math. 17 (1970), 192–208.

    Article  MathSciNet  Google Scholar 

  • [F] O. Forster, Über die Anzahl der Erzeugenden eines ideals in einem Noetherschen Ring, Math. Z. 84 (1964), 80–87.

    Article  MathSciNet  MATH  Google Scholar 

  • [GR] R. Gordon and J.C. Robson, Krull dimension, Mem. Amer. Math. Soc., 133 (1973).

    Google Scholar 

  • [Q] D. Quillen, Higher algebraic K-theory I, in Algebraic K-theory I: Higher K-theories, Lecture Notes in Math., No 341, Springer-Verlag, Berlin/New York, 1973.

    Google Scholar 

  • [RG] R. Rentschler and P. Gabriel, Sur la dimension des anneaux et ensembles ordonnés, C.R. Acad. Sci. Paris Sér. A 265 (1967), 712–715.

    MathSciNet  MATH  Google Scholar 

  • [Sm] P.F. Smith, On the dimension of group rings, Proc. London Math. Soc., 25 (1972), 288–302; Corrigendum, ibid, P. F. Smith, On the dimension of group rings, Proc. London Math. Soc., 27 (1973), 766–768.

    Article  MathSciNet  MATH  Google Scholar 

  • [St1] J.T. Stafford, Stable structure of noncommutative Noetherian rings, J. Algebra 47 (1977), 244–267.

    Article  MathSciNet  MATH  Google Scholar 

  • [St2] J.T. Stafford, Stable structure of noncommutative Noetherian rings, II, J. Algebra 52 (1978), 218–235.

    Article  MathSciNet  MATH  Google Scholar 

  • [St3] J.T. Stafford, Generating modules efficiently: algebraic K-theory for noncommutative Noetherian rings, J. Algebra 69 (1981), 312–346.

    Article  MathSciNet  MATH  Google Scholar 

  • [Sw1] R.G. Swan, The number of generators of a module, Math. Z. 102 (1967); 318–322.

    Article  MathSciNet  MATH  Google Scholar 

  • [Sw2] R.G. Swan, Algebraic K-theory, Lecture Notes in Math., No 76, Springer-Verlag, Berlin/New York, 1968.

    Book  MATH  Google Scholar 

  • [V] L.N. Vaseršteîn, On the stabilisation of the general linear group over a ring, Math USSR-Sb. 8 (1969), 383–400.

    Article  MathSciNet  MATH  Google Scholar 

  • [W] R.B. Warfield, Jr., The number of generators of a module over a fully bounded ring, J. Algebra 66 (1980), 425–447.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Marie-Paule Malliavin

Rights and permissions

Reprints and permissions

Copyright information

© 1982 Springer-Verlag

About this paper

Cite this paper

Stafford, J.T. (1982). Generating modules efficiently over noncommutative rings. In: Malliavin, MP. (eds) Séminaire d'Algèbre Paul Dubreil et Marie-Paule Malliavin. Lecture Notes in Mathematics, vol 924. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0092926

Download citation

  • DOI: https://doi.org/10.1007/BFb0092926

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11496-3

  • Online ISBN: 978-3-540-39188-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics