Number Field/Examples/Rational Numbers

Example of Number Field

The field of rational numbers $\Q$ is a number field.


Proof

From Rational Numbers form Subfield of Complex Numbers, $\Q$ is a subfield of $\C$.

Hence the result by definition of number field.

$\blacksquare$

Sources

  • 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $3$: Field Theory: Definition and Examples of Field Structure: $\S 88$
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