characteristic

《代数学引论》 · 第 129 页

如果幺环 $R$ 的单位元素 $e$ 生成的加法群 $G=\{ne\mid n\in\mathbb Z\}$ 是一个无限群，则 $R$ 叫做特征 $0$ 的环。

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《A Course in Finite Group Representation Theory》 · 第 85 页 · Section 3.1「The Characteristic of a Field」，Definition 1 及其前置定义

Given a ring $K$, there exists a unique ring homomorphism $\varphi:\mathbb Z\to K$, namely, the one characterized by $n\mapsto n\cdot 1$. Let $K$ be a field (or, more generally, an integral domain) and let $\varphi:\mathbb Z\to K$ be the canonical ring homomorphism discussed before. Furthermore, let $p\in\mathbb N$ be a generating element of the principal ideal $\ker\varphi$. Then $p$ is called the characteristic of $K$, and we write $p=\operatorname{char}K$.