╱🚧 inverse is unique
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代數 ⟩ 環 ⟩ unit
在 commutative ring with identity 內的非零元素 aaa 如果有乘法反元素 (multiplicative inverse) a−1{\color{orange}a^{-1}}a−1，則稱它為一個 unit。
M3：乘法反元素： aa−1=a−1a=1 (a≠0)a {\color{orange}a^{-1}} = {\color{orange}a^{-1}} a = \mathbf{1} \ (a \neq \mathbf{0})aa−1=a−1a=1 (a=0)
若一個元素的「乘法反元素」存在，則它必定是唯一的。（證明：🚧）
identity╱乘法單位元素
A field is a commutative ring with unity in which every nonzero element is a unit.
Contemporary Abstract Algebra (2017)
