Non-associative algebra

（重定向自Nonassociative ring）

A non-associative algebra (or distributive algebra) over a field K is a K-vector space A equipped with a binary multiplication operation which is K-bilinear A × A → A. Examples include Lie algebras, Jordan algebras, the octonions, and three-dimensional Euclidian space equipped with the cross product operation. Since it is not assumed that the multiplication is associative, using parentheses to indicate the order of multiplications is necessary. For example, the expressions (ab)(cd), (a(bc))d and a(b(cd)) may all yield different answers.

单词	Nonassociative ring
释义	Nonassociative ring 英语例句库 For nonassociative rings R with associative in the middle nucleus, R can be associative under some conditions. 摘要对结合子在中核心之非结合环R，在某些条件下R能够是结合的。英语百科 Non-associative algebra （重定向自Nonassociative ring） A non-associative algebra (or distributive algebra) over a field K is a K-vector space A equipped with a binary multiplication operation which is K-bilinear A × A → A. Examples include Lie algebras, Jordan algebras, the octonions, and three-dimensional Euclidian space equipped with the cross product operation. Since it is not assumed that the multiplication is associative, using parentheses to indicate the order of multiplications is necessary. For example, the expressions (ab)(cd), (a(bc))d and a(b(cd)) may all yield different answers.
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