Definition:Number Field
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Definition
A number field is a subfield of the field of complex numbers.
Examples
Rational Numbers
The field of rational numbers $\Q$ is a number field.
Real Numbers
The field of real numbers $\R$ is a number field.
Also see
- Results about number fields can be found here.
Sources
- 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $4$: Fields: $\S 17$. The Characteristic of a Field
- 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $3$: Field Theory: Definition and Examples of Field Structure: $\S 88$
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): number field
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): number field