代数数域
代数数域是数学中代数数论的基本概念，数域的一类，有时也被简称为数域，指有理数域![\mathbb{Q}](/Images/godic/202412/18/d45a4aa156a8ac07ab80e7d9cf5fa79f1728.png")
的有限扩张形成的扩域。任何代数数域都可以视作上的有限维矢量空间。
对代数数域的研究，或者更一般地说，对有理数域的代数扩张的研究，是代数数论的中心主题。
Algebraic number field
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Algebraic number field 代数数域
![Schematic depiction of ramification: the fibers of almost all points in Y below consist of three points, except for two points in Y marked with dots, where the fibers consist of one and two points (marked in black), respectively. The map f is said to be ramified in these points of Y.](/Images/godic/202412/18/Schematic_depiction_of_ramification.svg1728.png")
In mathematics, an algebraic number field (or simply number field) F is a finite degree (and hence algebraic) field extension of the field of rational numbers Q. Thus F is a field that contains Q and has finite dimension when considered as a vector space over Q.