An archimedean field is an ordered field that satisfies the archimedean property.
For $k$ a non-archimedean field for some non-archimedean absolute value ${\vert -\vert}$ one defines
its ring of integers to be
This is a local ring with maximal ideal
The residue field of $k$ is the quotient
Archimedean fields include
Non-archimedean fields include
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