Number field

A number field is a finite degree field extension of the field [math]\displaystyle{ \mathbb{Q} }[/math] of rational numbers.

The study of algebraic number fields, and, more generally, of algebraic extensions of the field of rational numbers, is the central topic of algebraic number theory.

Number Field Media

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  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.