Definition:Ring of Gaussian Integers

Definition

The ring of Gaussian integers $\struct {\Z \sqbrk i, +, \times}$ is the algebraic structure formed from:

the set of Gaussian integers $\Z \sqbrk i$

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 Number Field

Sources

• 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $5$: Rings: $\S 19$. Subrings: Example $33$
• 1970: B. Hartley and T.O. Hawkes: Rings, Modules and Linear Algebra ... (previous) ... (next): Chapter $1$: Rings - Definitions and Examples: $2$: Some examples of rings: Ring Example $5$