Galois Field has Non-Zero Characteristic
(Redirected from Finite Field has Non-Zero Characteristic)
Jump to navigation
Jump to search
Theorem
Let $\GF$ be a Galois field.
Then the characteristic of $\GF$ is non-zero.
Proof 1
A direct application of Characteristic of Finite Ring is Non-Zero.
$\blacksquare$
Proof 2
Let $\GF$ be a Galois field.
Let $P$ be its prime subfield.
Suppose $\Char \GF = 0$.
Then from Field of Characteristic Zero has Unique Prime Subfield, $P$ is isomorphic to $\Q$ which is infinite.
But a Galois field can not have an infinite subfield.
$\blacksquare$