finite extension

《代数学引论》 · 第 210 页

如果 $[K:F]<\infty$，则 $K/F$ 叫做有限扩张；否则，$K/F$ 叫做无限扩张。

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《A Course in Finite Group Representation Theory》 · 第 87 页 · Section 3.2「Finite and Algebraic Field Extensions」，Definition 1

Let $K\subset L$ be a field extension. Then the vector space dimension $[L:K]:=\dim_K L$ is called the degree of $L$ over $K$. The field extension is called finite or infinite, depending on whether $[L:K]$ is finite or infinite.