Hilbert’s Problem #12

Extension of Kroneker’s Theorem on Abelian Fields to Any Algebraic Realm of Rationality: Extend the Kronecker–Weber theorem on Abelian extensions of the rational numbers to any base number field.

With his 12th problem, Hilbert sought to generalize a theorem about the structure of certain extensions of the rational numbers to other number fields. It is currently unresolved.

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