Skip to main content

Nilpotent Elements in Semi-simple Jordan Algebras

  • Chapter
  • 658 Accesses

Part of the book series: Contemporary Mathematicians ((CM))

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. Albert, A. A.: “On Jordan algebras of linear transformations.” Trans. Amer. Math. Soc. 59, 524–555.

    Google Scholar 

  2. Albert, A. A.: “The Wedderburn principal theorem for Jordan algebras.” Annals of Math. 48, 1–7 (1947).

    Article  Google Scholar 

  3. Albert, A. A.: “A structure theory for Jordan algebras.” Annals of Math. 48, 446–467 (1947).

    Google Scholar 

  4. Albert, A. A.: “A theory of power associative commutative algebras.” Trans. Amer. Math. Soc. 69 503–527 (1950).

    Google Scholar 

  5. Albert, A. A., and N. Jacobson: “Reduced exceptional simple Jordan algebras.” Annals of Math. 66, 400–417 (1957).

    Article  Google Scholar 

  6. Cohn, P. M.: “Special Jordan algebras.” Canad. Journ. of Math. 6, 253–264 (1954).

    Article  Google Scholar 

  7. Freudenthal, H.: “Oktaven, Ausnahmegruppen and Oktavengeometrie.” Utrecht, 1951.

    Google Scholar 

  8. Harsri, B.: “Centralizers in Jordan algebras”, to appear in Pacific Journ. of Math.

    Google Scholar 

  9. Jacobson, F. D., and N. Jacobson: “Classification and representation of semi-simple Jordan algebras.” Trans. Amer. Math. Soc. 65, 141–169 (1949).

    Google Scholar 

  10. Jacobson, N. : “Theory of Rings.” Amer. Math. Soc. Surveys, vol. 2, New York, 1943.

    Google Scholar 

  11. Jacobson, N.: Completely reducible Lie algebras of linear transformations. Proc. Amer. Math. Soc. 2, 105–113 (1951).

    Article  Google Scholar 

  12. Jacobson, N. : “Structure of alternative and Jordan bimodules.” Osaka Math. Jour. 6, 1–70 (1954).

    Google Scholar 

  13. Jacobson, N.: “A theorem on the structure of Jordan algebras.” Proc. Nat. Acad. Sci. 42, 140–147 (1956).

    Article  Google Scholar 

  14. Jacobson, N.: “A note on three dimensional simple Lie algebras.” Indiana J. of Math, and Mech. 7, 823–832. (1958).

    Article  Google Scholar 

  15. Jacobson, N.: “Some groups of transformations defined by Jordan algebras”, I and II, forthcoming in Journal für r. u. angew. Math.

    Google Scholar 

  16. Jacobson, N., and L. J. Paige: “Jordan algebras with two generators.” Indiana J. of Math. and Mech. 6, 895–906 (1957).

    Article  Google Scholar 

  17. Malcev, A. I.: “Foundations of Linear Algebra” (Russian), Moscow-Leningrad, 1947.

    Google Scholar 

  18. Penico, A. J.: “The Wedderburn principal theorem for Jordan algebras.” Trans. Amer. Math. Soc. 70, 404–421 (1951).

    Article  Google Scholar 

  19. Schafer, R. D.: “The exceptional simple Jordan algebras.” Amer. J. of Math. 70, 82–94 (1948).

    Article  Google Scholar 

  20. Shirshov, A. I.: “On special J-rings.” Math. Sbornik. 38, (80), 149–160 (1956).

    Google Scholar 

  21. Taft, E.: “Invariant Wedderburn factors”, Illinois Journ. of Math. 1, 565–573 (1957).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Birkhäuser Boston

About this chapter

Cite this chapter

Jacobson, N. (1989). Nilpotent Elements in Semi-simple Jordan Algebras. In: Nathan Jacobson Collected Mathematical Papers. Contemporary Mathematicians. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-3694-8_25

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-3694-8_25

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-8215-0

  • Online ISBN: 978-1-4612-3694-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics