運算 ⟩ 二元運算 ⟩ 結合律 (associativity)
若一個二元運算「 ∗{\color{orange}\ast}∗ 」擁有以下性質:
(a∗b)∗c=a∗(b∗c)(a {\color{orange}\ast} b ) {\color{orange}\ast} c = a {\color{orange}\ast} (b {\color{orange}\ast} c )(a∗b)∗c=a∗(b∗c)
我們就說此運算具有「結合律」(associativity)。
「Group╱群」的運算具有「結合律」。
一個擁有「結合律」的「代數系統」稱為「半群」(semigroup)。
Abstract and Linear Algebra (Burton) ⟩ 2.1 Definition and Elementary Properties of Groups (p. 43, 44)
Understanding Analysis ⟩ 8.6 A Construction of R From Q, Def. 8.6.4 (p.299)
Last updated 1 year ago
Was this helpful?