Vipul: Created page with '{{field property}} ==Definition== A '''number field''' is a field that is a finite extension of the field of rational numbers. ==Relation with other properties== ...'

2009-05-14T22:31:39Z

Created page with '{{field property}} ==Definition== A '''number field''' is a field that is a finite extension of the field of rational numbers. ==Relation with other properties== ...'

New page

{{field property}}

==Definition==

A '''number field''' is a [[field]] that is a [[finite extension]] of the [[field of rational numbers]].

==Relation with other properties==

===Stronger properties===

* [[Weaker than::Galois number field]]

==Metaproperties==

{{subfield-closed}}

A subfield of a number field is again a number field.

{{composite-closed}}

If <math>K_1</math> and <math>K_2</math> are subfields of a field <math>K</math>, and both <math>K_1</math> and <math>K_2</math> are number fields, then so is the composite field <math>K_1K_2</math>.

{{finite-extension-closed}}

Any finite extension of a number field is a number field.

Number field - Revision history

Vipul: Created page with '{{field property}} ==Definition== A '''number field''' is a field that is a finite extension of the field of rational numbers. ==Relation with other properties== ...'