Field of characteristic zero

This article defines a field property: a property that can be evaluated to true/false for any field.
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Definition

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

1. It is a field whose prime subfield is the field of rational numbers.
2. It is a field containing the field of rational numbers.
3. It is a field such that, for any natural number $n$, the field element $n$ (obtained by adding $1$ to itself $n$ times) is not zero.

Relation with other properties

Stronger properties

• Algebraically closed field of characteristic zero
• Archimedean field
• Real-closed field
• Euclidean field
• Formally real field

Weaker properties

• Perfect field