We study the polynomial identities of alternative and Jordan algebras which imply the nilpotency of the algebras. In the case of a field of characteristic 0 we describe all these systems of identities as well as all almost nilpotent varieties of alternative and Jordan algebras. In particular, we establish a connection between the Engel identity for the Lie algebras and the standard identity for the Jordan algebras.

中文翻译：

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代数和约旦代数的幂等性

我们研究了交替代数和约旦代数的多项式恒等式，这暗示了代数的幂等性。在特征为0的字段中，我们描述所有这些恒等式系统以及所有几乎幂等的代数和约旦代数。特别是，我们在李代数的恩格尔身份和约旦代数的标准身份之间建立了联系。