Section 33 Finite Fields

NOTE

All finite fields must have prime-power order. They are all referred to as the Galois field of order $p^n$, or simply $GF(p^n)$

33.1 Theorem

A First Course in Abstract Algebra, p.300

Let $E$ be a finite extension of degree $n$ over a finite field $F$. If $F$ has $q$ elements, then $E$ has $q^n$ elements