Number Fields
《Number Fields》 · 第 22 页 · Chapter 2，关于数环 $R$ 为秩 $n$ 自由 Abel 群的 Corollary 后
Equivalently, $R$ has a basis over $\mathbb Z$: There exist $\beta_1,\ldots,\beta_n\in R$ such that every $\alpha\in R$ is uniquely representable in the form $m_1\beta_1+\cdots+m_n\beta_n$, $m_i\in\mathbb Z$. $\{\beta_1,\ldots,\beta_n\}$ is called an integral basis for $R$, or a basis for $R$ over $\mathbb Z$.