Abstract
We show that, unlike alternative algebras, prime quotients of a nondegenerate Jordan system or a Lie algebra need not be nondegenerate, even if the original Jordan system is primitive, or the Lie algebra is strongly prime, both with nonzero simple hearts. Nevertheless, for Jordan systems and Lie algebras directly linked to associative systems, we prove that even semiprime quotients are necessarily nondegenerate.
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J. A. Anquela, T. Cortés, E. García: Partly supported by the Ministerio de Ciencia e Innovacion and Fondos FEDER, MTM2010-16153, the Ministerio de Economia y Competitividad and Fondos FEDER, MTM2014-52470-P, and the Junta de Andalucia FQM-264.
M. Gómez Lozano: Partly supported by the Ministerio de Ciencia e Innovacion and Fondos FEDER, MTM2010-19482, the Ministerio de Economia y Competitividad and Fondos FEDER, MTM2014-52470-P, and the Junta de Andalucia FQM-264.
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Anquela, J.A., Cortés, T., García, E. et al. Prime Quotients of Jordan Systems and Lie Algebras. Mediterr. J. Math. 13, 29–52 (2016). https://doi.org/10.1007/s00009-014-0488-9
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DOI: https://doi.org/10.1007/s00009-014-0488-9