Galois Field/Examples/Field of Integers Modulo Prime

Example of Galois Field

The field of integers modulo $p$ is a Galois field:

Let $p \in \Bbb P$ be a prime number.

Let $\Z_p$ be the set of integers modulo $p$.

Let $+_p$ and $\times_p$ denote addition modulo $p$ and multiplication modulo $p$ respectively.

The algebraic structure $\struct {\Z_p, +_p, \times_p}$ is the field of integers modulo $p$.

Proof

See Ring of Integers Modulo Prime is Field.

Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Galois field (finite field)