Definition:Cyclotomic Ring
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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.