Galois Field/Examples/Field of Integers Modulo Prime
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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)