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单词 Alternative algebra
释义

Alternative algebra

中文百科

交错代数

在抽象代数中,交错代数是乘法不满足结合性,仅满足交错性的代数。也就是说,我们有:

  • x(xy) = (xx)y
  • (yx)x = y(xx)

对于所有代数中的xy。每一个结合代数都显然是交错的,但有些严格的非结合代数,例如八元数,也是交错的。另一方面,十六元数则不是交错的。

英语百科

Alternative algebra 交错代数

In abstract algebra, an alternative algebra is an algebra in which multiplication need not be associative, only alternative. That is, one must have

for all x and y in the algebra.

Every associative algebra is obviously alternative, but so too are some strictly non-associative algebras such as the octonions. The sedenions, on the other hand, are not alternative.

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更新时间:2025/6/23 16:12:06