group of units

《代数学引论》 · 第 46 页

显然幺环 $L$ 的全部单位构成的集合对乘法成一群，称为 $L$ 的单位群。

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《Compact Lie Groups》 · 第 226 页 · Chapter 3，Section 3.1「First Properties」，Definition

If $R$ is a commutative ring, then the group of units of $R$ is $U(R)=\{\text{all units in }R\}$. It is easy to check that $U(R)$ is a multiplicative group; that is, it is closed under products and inverses.