- #1
Elzair
- 11
- 0
Homework Statement
Let E be an extension of a finite field F, where F has q elements. Let [tex]\alpha \epsilon E[/tex] be algebraic over F of degree n. Prove [tex]F \left( \alpha \right)[/tex] has [tex]q^{n}[/tex] elements.
Homework Equations
An element [tex]\alpha[/tex] of an extension field E of a field F is algebraic over F if [tex]f \left( \alpha \right) = 0[/tex] for some nonzero [tex]f\left(x\right) \epsilon F[x][/tex].
The Attempt at a Solution
I do not know how to begin. Is [tex]F \left( \alpha \right)[/tex] a simple extension field?