It is proved that all Jordan s-identities in three variables are consequences of the Glennie s-identity.
Similar content being viewed by others
References
K. A. Zhevlakov, A. M. Slin’ko, I. P. Shestakov, and A. I. Shirshov, Rings That Are Nearly Associative [in Russian], Nauka, Moscow (1978).
A. A. Albert and L. J. Paige, “On homomorphism property of a certain Jordan algebras,” Trans. Am. Math. Soc., 93, 20–29 (1959).
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).
K. McCrimmon, “A not-so-natural s-identity,” Comm. Alg., 15, 2099–2118 (1987).
A. Thedy, “A natural s-identity of Jordan algebras,” Comm. Alg., 15, 2081–2098 (1987).
Yu. A. Medvedev, “Free Jordan algebras,” Algebra Logika, 27, No. 2, 172–200 (1988).
K. McCrimmon, A Taste of Jordan Algebras, Universitext, Springer, New York (2004).
The Dniester Notebook. Unsolved Problems in Ring Theory [in Russian], 4th edn, Institute of Mathematics SO RAN, Novosibirsk (1993).
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).
Author information
Authors and Affiliations
Corresponding author
Additional information
*Supported by FAPESP (grant No. 2010/50171-8/).
Translated from Algebra i Logika, Vol. 50, No. 1, pp. 89–121, January–February, 2011.
Rights and permissions
About this article
Cite this article
Sverchkov, S.R. Jordan s-identities in three variables. Algebra Logic 50, 62–88 (2011). https://doi.org/10.1007/s10469-011-9124-y
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10469-011-9124-y