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Abstract
Abstract Each subdivision within the cyclotomic domain constitutes an Abelian numerical field, and Kronecker established the reverse of this statement. His aspirations extended beyond the realm of rational numbers, delving into the Abelian extensions of imaginary quadratic numerical fields and introducing the renowned jugendtraum. It wasn’t until the emergence of class field theory in the 20th century that this youthful dream was confirmed as valid. This concept also maintains a close connection to Hilbert’s 12th problem, which remains unresolved to this day.
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