Skip to main content

The structure of noetherian rings

Part of the Lecture Notes in Mathematics book series (LNM,volume 246)

Keywords

  • Prime Ideal
  • Local Ring
  • Maximal Ideal
  • Left Ideal
  • Prime Ring

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S. A. Amitsur, Prime rings having polynomial identities with arbitrary coefficients, Proc. London Math. Soc., (3), 17, 1967, 470–486.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. J. E. Björk, Conditions which imply that subrings of Artinian rings are Artinian, J. Algebra (to appear).

    Google Scholar 

  3. N. Bourbaki Algèbre commutative XXVII, Hermann, Paris.

    Google Scholar 

  4. H. Cartan and S. Eilenberg, Homological Algebra, Princeton, 1956.

    Google Scholar 

  5. D. Eisenbud and J. C. Robson, Modules over Dedekind prime rings, J. Algebra 16(1970), 67–85.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. _____, Hereditary Noetherian prime rings, J. Algebra, 16(1970), 86–104.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. P. Gabriel, Des catégories abéliennes, Thèse 1962.

    Google Scholar 

  8. P. Gabriel and R. Rentschler, Sur la dimension des anneaux er ensembles ordonnés, C. R. Acad. Sci., Paris, 265(1967), 712–715.

    MathSciNet  MATH  Google Scholar 

  9. A. W. Goldie, The structure of prime rings under ascending chain conditions, Proc London Math. Soc., 8(1958), 589–608.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. A. W. Goldie, Semi-prime rings with maximum condition, Proc. London Math. Soc.,10(1960), 201–220.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. A. W. Goldie, Torsion-free modules and rings, J. Algebra (1964), 268–287.

    Google Scholar 

  12. _____, Localization in non-commutative Noetherian rings, J Algebra 5(1967), 89–105.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. _____, A note on non-commutative localization, J. Algebra 8(1968), 41–44.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. _____, Some aspects of ring theory, Bull. London Math. Soc., 1(1969), 129–154.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. W. D. Gwynne and J. C. Robson, Completions of Dedekind prime rings, (to appear).

    Google Scholar 

  16. R. Hart, Krull dimension and global dimension of simple Ore-extensions, Math. Zeit. (to appear).

    Google Scholar 

  17. C. R. Hajamavis and T. H. Lenagan, Localization in asano orders (to appear).

    Google Scholar 

  18. Y. Hinohari, Notes on non-commutative local rings, Nagoya Math. J., 17(1960), 161–166.

    CrossRef  MathSciNet  Google Scholar 

  19. N. Jacobson, The theory of rings, Amer. Math. Soc. Surveys, VI(New York, 1943).

    Google Scholar 

  20. _____, Structure of rings, Amer Math. colloq. Publ., 37(1956, 1964).

    Google Scholar 

  21. _____, Lie algebras, Interscience (New York, 1962).

    Google Scholar 

  22. I. Kaplansky, Fields and Rings, Univ. of Chicago Press, 1969.

    Google Scholar 

  23. J. Lambek, Lectures on rings and modules, Blaisdell, 1966.

    Google Scholar 

  24. _____, Torsion theories, Springer lecture notes 177.

    Google Scholar 

  25. T. H. Lenagan, Bounded asano orders are hereditary, (to appear).

    Google Scholar 

  26. J. C. McConnell, The intersection theorem for a class of non-commutative rings, (3) 17(1967), 487–498.

    Google Scholar 

  27. _____, Localization in enveloping rings, J. London Math. Soc., 43(1968), 421–428.

    CrossRef  MathSciNet  MATH  Google Scholar 

  28. A. Malcev, On the immersion of an algebraic ring into a field, Math. Ann., 113(1936), 686–691.

    CrossRef  MathSciNet  MATH  Google Scholar 

  29. G. O. Michler, Maximal asano orders, Proc. London Math. Soc., (3), 19(1969), 421–443.

    CrossRef  MathSciNet  MATH  Google Scholar 

  30. _____, Primringe mit Krull-dimension eins, J. für. r.u. angewandte Math., 239 (240), (1970), 366–381.

    MathSciNet  MATH  Google Scholar 

  31. J. C. Robson, Non-commutative Dedekind rings, J. Algebra, 9(1968), 249–265.

    CrossRef  MathSciNet  MATH  Google Scholar 

  32. _____, Idealizers and hereditary Noetherian prime rings, J. of Algebra, (to appear).

    Google Scholar 

  33. L. W. Small, On some questions in Noetherian rings, Bull. Amer. Math. Soc., 72(1966), 853–857.

    CrossRef  MathSciNet  MATH  Google Scholar 

  34. L. W. Small, Orders in Artinian rings, J. Algebra 4(1966), 13–41.

    CrossRef  MathSciNet  MATH  Google Scholar 

  35. _____, Semi-hereditary rings, Bull. Amer. Math. Soc., 73(1967), 656–658.

    CrossRef  MathSciNet  MATH  Google Scholar 

  36. D. Webber, Ideals and modules of simple Noetherian hereditary rings, (to appear).

    Google Scholar 

  37. O. Zariski and P. Samuel, Commutative algebra I, II, Van Nostrand, 1960.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and Permissions

Copyright information

© 1972 Springer-Verlag

About this paper

Cite this paper

Goldie, A.W. (1972). The structure of noetherian rings. In: Lectures on Rings and Modules. Lecture Notes in Mathematics, vol 246. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0059567

Download citation

  • DOI: https://doi.org/10.1007/BFb0059567

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-05760-4

  • Online ISBN: 978-3-540-37181-6

  • eBook Packages: Springer Book Archive