[[Mathematics MOC]]
# Algebraic number theory MOC

**Algebraic number theory** is the study of integers, i.e. [[Number theory MOC|number theory]], via the study of things _bigger_ than the integers, i.e. [[Ring theory MOC|ring theory]] and [[Field theory MOC|field theory]].
The central objects are the [[number field]] and its [[Algebraic integer|ring of integers]].
In particular, we study

- [[Quadratic field]] with the [[Quadratic integers]].
- [[Cyclotomic field]] with the [[Cyclotomic integers]].

## Geometry of numbers

- [[Minkowski's convex body theorem]]
- [[Minkowski embedding]], [[Minkowski's bound]]
- [[Logarithmic embedding]], [[Dirichlet's unit theorem]]

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