Vipul: Created page with '{{field property}} ==Definition== A '''field of characteristic zero''' is defined in the following equivalent ways: # It is a field whose prime subfield is the [[defining ingr...'

2009-05-14T22:06:47Z

Created page with '{{field property}} ==Definition== A '''field of characteristic zero''' is defined in the following equivalent ways: # It is a field whose prime subfield is the [[defining ingr...'

New page

{{field property}}

==Definition==

A '''field of characteristic zero''' is defined in the following equivalent ways:

# It is a field whose prime subfield is the [[defining ingredient::field of rational numbers]].
# It is a field containing the [[field of rational numbers]].
# It is a field such that, for any natural number <math>n</math>, the field element <math>n</math> (obtained by adding <math>1</math> to itself <math>n</math> times) is not zero.

==Relation with other properties==

===Stronger properties===

* [[Weaker than::Algebraically closed field of characteristic zero]]
* [[Weaker than::Archimedean field]]
* [[Weaker than::Real-closed field]]
* [[Weaker than::Euclidean field]]
* [[Weaker than::Formally real field]]

===Weaker properties===

* [[Stronger than::Perfect field]]

Field of characteristic zero - Revision history

Vipul: Created page with '{{field property}} ==Definition== A '''field of characteristic zero''' is defined in the following equivalent ways: # It is a field whose prime subfield is the [[defining ingr...'