Algebra and Logic

, Volume 50, Issue 1, pp 62–88

Jordan s-identities in three variables


It is proved that all Jordan s-identities in three variables are consequences of the Glennie s-identity.


Jordan s-identities free Jordan algebras free special Jordan algebras 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    K. A. Zhevlakov, A. M. Slin’ko, I. P. Shestakov, and A. I. Shirshov, Rings That Are Nearly Associative [in Russian], Nauka, Moscow (1978).Google Scholar
  2. 2.
    A. A. Albert and L. J. Paige, “On homomorphism property of a certain Jordan algebras,” Trans. Am. Math. Soc., 93, 20–29 (1959).CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    C. M. Glennie, “Some identities valid in special Jordan algebras but not valid in all Jordan algebras,” Pac. J. Math., 16, No. 1, 47–59 (1966).MATHMathSciNetGoogle Scholar
  4. 4.
    K. McCrimmon, “A not-so-natural s-identity,” Comm. Alg., 15, 2099–2118 (1987).CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    A. Thedy, “A natural s-identity of Jordan algebras,” Comm. Alg., 15, 2081–2098 (1987).CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Yu. A. Medvedev, “Free Jordan algebras,” Algebra Logika, 27, No. 2, 172–200 (1988).MATHGoogle Scholar
  7. 7.
    K. McCrimmon, A Taste of Jordan Algebras, Universitext, Springer, New York (2004).Google Scholar
  8. 8.
    The Dniester Notebook. Unsolved Problems in Ring Theory [in Russian], 4th edn, Institute of Mathematics SO RAN, Novosibirsk (1993).Google Scholar
  9. 9.
    S. R. Sverchkov, “The Lie algebra of skew-symmetric elements and its application in the theory of Jordan algebras,” Sib. Mat. Zh., 51, No. 3, 626–637 (2010).MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  1. 1.Novosibirsk State UniversityNovosibirskRussia

Personalised recommendations