# Definition:Algebraic Number Theory

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## Contents

## Definition

**Algebraic number theory** is the branch of abstract algebra which studies structures in which the usual number fields are embedded.

As such it can also be considered to be a branch of number theory.

## Also see

- Results about
**algebraic number theory**can be found here.

## Historical Note

The field of algebraic number theory was initiated by Carl Friedrich Gauss, with his papers of $1828$ and $1832$ on biquadratic residues.

## Sources

- 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next): Entry:**algebraic number theory** - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {B}.16$: The Sequence of Primes