×

Surjective quadratic Jordan algebras. (English) Zbl 1474.17046

Summary: We introduce the concepts of surjectivity and linear minimality for quadratic Jordan algebras, then we present a partial classification of such algebras of characteristic 2. As a corollary, we obtain that in substance non-trivial minimal quadratic Jordan algebras are fields.

MSC:

17C10 Structure theory for Jordan algebras

References:

[1] 421-427 · Zbl 0101.18604
[2] E. R. Baisalov, K. A. Meirembekov, A. T. Nurtazin, “Definable minimal models”, Model Theory in Kazakhstan, EcoStudy, Almaty, 2006, 140-157
[3] 105-110 · Zbl 1285.03035
[4] E. R. Baisalov, R. Bibazarov, B. Duzban, “Linear minimal associative rings”, Bulletin of the L. N. Gumilyov Eurasian National University (math., comp. sci., mech. series), 89 (2012), 32-35 (in Kazakh)
[5] N. Jacobson, Lie algebras, Wiley, Sons, New York etc, 1962 · Zbl 0121.27504
[6] N. Jacobson, Lectures on quadratic jordan algebras, Tata Institute of Fundamental research, Bombay, 1962
[7] K. McCrimmon, A taste of Jordan algebras, Springer, New York, 2004 · Zbl 1044.17001
[8] K. McCrimmon, “Quadratic Jordan algebras and cubing operations”, Trans. of the Amer. Math. Soc., 153 (1971), 265-278 · Zbl 0226.17007
[9] E. I. ZelTmanov, “Jordan division algebras”, Algebra and Logic, 18 (1979), 286-310 (in Russian) · Zbl 0433.17010
[10] K. A. Zhevlakov, A. M. Slinko, I. P. Shestakov, A. I. Shirshov, Rings that are nearly associative, Pure and Applied Mathematics, 104, Academic Press, 1982 · Zbl 0487.17001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.