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单词 Power associative algebra
释义

Power associative algebra

中文百科

幂结合性 Power associativity

(重定向自Power associative algebra)

抽象代数中,幂结合性是弱结合律。

如果由任意元素所产生的次代数符合结合律,这个代数就是拥有幂结合性。元素x能够多次自乘并不在乎到达了什幺幂数。例如x(x(xx)) = (x(xx))x = (xx)(xx). 以下结合律方式更为强烈:

代数中每个x, (xx)x = x(xx)

每个结合性的代数都明显地拥有幂结合性,一些交错代数(例如八元数)甚至是一些非交错代数(例如十六元数)亦如此。

英语百科

Power associativity 幂结合性

(重定向自Power associative algebra)

In abstract algebra, power associativity is a property of a binary operation which is a weak form of associativity.

An algebra (or more generally a magma) is said to be power-associative if the subalgebra generated by any element is associative. Concretely, this means that if an element x is multiplied by itself several times, it doesn't matter in which order the multiplications are carried out, so for instance x(x(xx)) = (x(xx))x = (xx)(xx).

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更新时间:2025/6/22 16:36:05