Skip to main content
SpringerLink
Log in

Balanced rings

  • Conference paper
  • First Online:
Lectures on Rings and Modules

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

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 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.

IV. References

  1. BASS, H. Algebraic K-theory. Benjamin, New York, 1968.

    MATH  Google Scholar 

  2. BOURBAKI, N. Algèbre, Ch. VIII. Hermann, Paris, 1958.

    MATH  Google Scholar 

  3. CAMILLO, V. P. Balanced rings and a problem of Thrall. Trans. Amer. Soc. 149 (1970), 143–153.

    Article  MathSciNet  MATH  Google Scholar 

  4. CAMILLO, V. P. AND FULLER, K. R. Balanced and QF-1 algebras. To appear.

    Google Scholar 

  5. COHN, P. M. Quadratic extensions of skew fields. Proc. London Math. Soc. 11 (1961), 531–556.

    Article  MathSciNet  MATH  Google Scholar 

  6. CUNNINGHAM, R. S. AND RUTTER, E. A., JR. The double centralizer property is categorical. To appear.

    Google Scholar 

  7. CURTIS, C. W. AND REINER, I. Representation theory of finite groups and associative algebras, Interscience Publ., New York, 1962.

    MATH  Google Scholar 

  8. DICKSON, S. E. AND FULLER, K. R. Commutative QF-1 rings are QF. Proc. Amer. Math. Soc. 24 (1970), 667–670.

    MathSciNet  MATH  Google Scholar 

  9. DLAB, V. AND RINGEL, C. M. Rings with the double centralizer property. To appear.

    Google Scholar 

  10. DLAB, V. AND RINGEL, C. M. On a class of balanced non-uniserial rings. Math. Ann. To appear.

    Google Scholar 

  11. DLAB, V. AND RINGEL, C. M. Balanced local rings with commutative residue fields. To appear.

    Google Scholar 

  12. DLAB, V. AND RINGEL, C. M. The structure of balanced rings. To appear.

    Google Scholar 

  13. DLAB, V. AND RINGEL, C. M. Exceptional rings. To appear.

    Google Scholar 

  14. FLOYD, D. R. On QF-1 algebras. Pacific J. 27 (1968), 81–94.

    Article  MathSciNet  MATH  Google Scholar 

  15. FULLER, K. R. Double centralizers of injectives and projectives over artinian rings. Illinois J. 14 (1970), 658–664.

    MathSciNet  MATH  Google Scholar 

  16. FULLER, K. R. Primary rings and double centralizers. Pacific J. 34 (1970), 379–383.

    Article  MathSciNet  MATH  Google Scholar 

  17. JACOBSON, N. Structure of rings. Coll. Publ. Amer. Math. Soc., Vol. 37, 1956.

    Google Scholar 

  18. JANS, J. P. On the double centralizer condition. Math. Ann. 188 (1970), 85–89.

    Article  MathSciNet  Google Scholar 

  19. MORITA, K. Duality for modules and its application to the theory of rings with minimum condition. Sci. Rep. Tokyo Kyoiku Daigaku, Sec. A 6 (1958), 83–142.

    MathSciNet  MATH  Google Scholar 

  20. MORITA, K. On algebras for which every faithful representation is its own second commutator. Math. Z. 69 (1958), 429–434.

    Article  MathSciNet  MATH  Google Scholar 

  21. MORITA, K. AND TACHIKAWA, H. On QF-3 rings. To appear.

    Google Scholar 

  22. NAKAYAMA, T. On Frobeniusean algebras. II. Ann. of Math. 42 (1941), 1–21.

    Article  MathSciNet  MATH  Google Scholar 

  23. NESBITT, C. J. AND THRALL, R. M. Some rings theorems with applications to modular representations. Ann. of Math. 47 (1946), 551–567.

    Article  MathSciNet  MATH  Google Scholar 

  24. TACHIKAWA, H. Duality theorem of character modules for rings with minimum condition. Math. Z. 68 (1958), 479–487.

    Article  MathSciNet  MATH  Google Scholar 

  25. TACHIKAWA, H. On rings for which every indecomposable right module has a unique maximal submodule. Math. Z. 71 (1959), 200–222.

    Article  MathSciNet  MATH  Google Scholar 

  26. TACHIKAWA, H. Double centralizers and dominant dimensions. Math. Z. 116 (1970), 79–88.

    Article  MathSciNet  MATH  Google Scholar 

  27. THRALL, R. M. Some generalizations of quasi-Frobenius algebras. Trans. Amer. Math. Soc. 64 (1948), 173–183.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Carleton University, Ottawa, Canada

    Vlastimil Dlab & Claus Michael Ringel

Authors
  1. Vlastimil Dlab
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Claus Michael Ringel
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1972 Springer-Verlag

About this paper

Cite this paper

Dlab, V., Ringel, C.M. (1972). Balanced rings. In: Lectures on Rings and Modules. Lecture Notes in Mathematics, vol 246. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0059564

Download citation

  • DOI: https://doi.org/10.1007/BFb0059564

  • 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

Publish with us

Policies and ethics

Search

Navigation