Prime Quotients of Jordan Systems and Lie Algebras |
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| Authors: | José A Anquela Teresa Cortés Esther García Miguel Gómez Lozano |
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| Institution: | 1.Departamento de Matemáticas,Universidad de Oviedo,Oviedo,Spain;2.Departamento de Matemática Aplicada, Ciencia e Ingeniería de los Materiales y Tecnología Electrónica,Universidad Rey Juan Carlos,Móstoles,Spain;3.Departamento de álgebra, Geometría y Topología,Universidad de Málaga,Málaga,Spain |
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| 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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