III.63 Number Fields: Page 254.

Number Fields.

A number field K is a finite-degree field extension of the field of rational numbers.

The simplest are the quadratic fields.

A number is an algebraic integer of the number field if it is a root of a monic polynomial with coefficients in the usual Integers, Z.  One may embed fields into Ideals.  The Ideals maintain the unique factorization into integers.

Dirichlet’s unit theorem.

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