\begin{definition}[Definition:Cyclotomic Ring]
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'''.
{{Proofread|Seriously unsure about this. Picked the name by back formation from Definition:Cyclotomic Field and found a tiny number of papers on the internet referring to such a construct by that name. "Ring of integers on cyclotomic field" is another way of describing it. The book I'm working through provides the example $\Z \sqbrk {i \sqrt 5}$ in one of its final few exercises so its coverage it sketchy. Does anyone know about this?}}
\end{definition}