Skip to main content
Log in

Absolute zero-divisors and algebraic Jordan algebras

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

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.

Literature Cited

  1. A. I. Kostrikin, “On Burnside's problem,” Izv. Akad. Nauk SSSR, Ser. Mat.,23, No. 1, 3–34 (1959).

    Google Scholar 

  2. A. I. Kostrikin, “Sandwiches in Lie algebras,” Mat. Sb.,110, No. 1, 3–12 (1979).

    Google Scholar 

  3. V. G. Skosyrskii, “Jordan algebras with the minimal condition of two-sided ideals,” Preprint, Institute of Mathematics, Siberian Branch, Academy of Sciences of the USSR, Novosibirsk (1981).

    Google Scholar 

  4. A. I. Shirshov, “On some nonassociative nil-rings and algebraic algebras,” Mat. Sb.,41, No. 3, 381–394 (1957).

    Google Scholar 

  5. Dnestr Notebook: Unsolved Problems of Ring Theory [in Russian], Institute of Mathematics, Siberian Branch, Academy of Sciences of the USSR, Novosibirsk (1976).

  6. E. I. Zel'manov, “Jordan algebras with a finiteness condition,” Algebra Logika,17, No. 6, 693–703 (1978).

    Google Scholar 

  7. K. McCrimmon, “The Zelmanov nilpotence theorem for quadratic Jordan algebras,” J. Algebra,63, No. 1, 76–97 (1980).

    Google Scholar 

  8. A. I. Mal'cev, Algebraic Systems, Springer-Verlag, Berlin-Heidelberg-New York (1973).

    Google Scholar 

  9. E. I. Zel'manov, “Absolute zero-divisors in Jordan pairs and in Lie algebras,” Mat. Sb.,117, No. 4, 611–629 (1980).

    Google Scholar 

  10. M. Koecher, “Imbedding of Jordan algebras into Lie algebras. I,” Am. J. Math.,89, No. 3, 787–816 (1967).

    Google Scholar 

  11. N. Jacobson, Lie Algebras, Interscience (1962).

  12. K. A. Zhevlakov, A. M. Slin'ko, I. P. Shestakov, and A. I. Shirshov, Rings That Are Close to Being Assoaciative [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  13. E. I. Zel'manov, “On prime Jordan algebras,” Algebra Logika,18, No. 2, 162–175 (1979).

    Google Scholar 

  14. S. A. Amitsur, “Identities in rings with involutions,” Israel J. Math.,7, No. 1, 63–68 (1969).

    Google Scholar 

  15. N. Jacobson, Structure of Rings, American Mathematical Society, Providence, R. I. (1956).

    Google Scholar 

  16. K. McCrimmon, “A characterization of the radical of a Jordan algebra,” J. Algebra,18, No. 1, 103–111 (1971).

    Google Scholar 

  17. K. McCrimmon, “Zelmanov's prime theorem for quadratic Jordan algebras,” Preprint, Univ. of Virginia, Charlottesville (1980).

    Google Scholar 

  18. N. Jacobson, Structure and Representations of Jordan Algebras, American Mathematical Society, Providence, R. I. (1968).

    Google Scholar 

  19. K. A. Zhevlakov and I. P. Shestakov, “On local finiteness in the sense of Shirshov,” Algebra Logika,12, No. 1, 41–73 (1973).

    Google Scholar 

  20. L. H. Rowen, “Nonassociative rings satisfying normal polynomial identities,” J. Algebra,49, No. 1, 104–111 (1977).

    Google Scholar 

  21. I. P. Shestakov, “Finite-dimensional algebras with a nil-basis,” Algebra Logika,10, No. 1, 87–99 (1971).

    Google Scholar 

Download references

Authors

Additional information

Institute of Mathematics, Siberian Branch, Academy of Sciences of the USSR. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 23, No. 6, pp. 100–116, November–December, 1982.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zel'manov, E.I. Absolute zero-divisors and algebraic Jordan algebras. Sib Math J 23, 841–854 (1982). https://doi.org/10.1007/BF00968754

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00968754

Keywords

Navigation