Definition:Ring of Gaussian Integers

Definition
The ring of Gaussian integers $\left({\Z \left[{i}\right], +, \times}\right)$ is the algebraic structure formed from:


 * the set of Gaussian integers $\Z \left[{i}\right]$
 * the operation of complex addition
 * the operation of complex multiplication.

Also see

 * Gaussian Integers form Subring of Complex Numbers
 * Gaussian Integers form Integral Domain

Generalization

 * Definition:Ring of Integers of a Number Field