# Definition:Cyclotomic Ring

## Definition

Let $\Z \sqbrk {i \sqrt n}$ be the set $\set {a + i b \sqrt n: a, b \in \Z}$.

The algebraic structure $\struct {\Z \sqbrk {i \sqrt n}, +, \times}$ is the $n$th cyclotomic ring.

## Examples

### $5$th Cyclotomic Ring

The $5$th cyclotomic ring is the algebraic structure:

$\struct {\Z \sqbrk {i \sqrt 5}, +, \times}$

where $\Z \sqbrk {i \sqrt 5}$ is the set $\set {a + i b \sqrt 5: a, b \in \Z}$.

$\struct {\Z \sqbrk {i \sqrt 5}, +, \times}$ is a ring.

## Also see

• Results about cyclotomic rings can be found here.