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A finite field extension of the rational numbers.
wp-number-fieldnlab-number-fieldmilne-algebraic-number-theoryEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Require characteristic zero and finite dimension over the canonically embedded prime field .
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
nlab-number-fieldmilne-algebraic-number-theoryEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
A number field has Archimedean places from embeddings and non-Archimedean places associated with prime ideals, understood as equivalence classes of absolute values.
Apply a standard functorial or canonical construction whose output is not merely a reduct of the input and is not generally an equivalent presentation of the same object.
milne-algebraic-number-theoryThis is an authored directed relation from the source endpoint to the target endpoint.
Select the elements integral over ; they form the ring of integers.
Apply a standard functorial or canonical construction whose output is not merely a reduct of the input and is not generally an equivalent presentation of the same object.
wp-ring-integersmilne-algebraic-number-theory