Field Power
 |
 Carver PM 15 Magnetic Field Power Amplifier  US $46.00
|
| Pro Audio Equipment Blog |
How do you prove that a power of an algebraic number over a field is also an algebraic number?
This question is in Abstract Algebra.
If you have an algebraic element 'a' over a field F, and some integer n, how can you prove 'a to the n power' is also an algebraic element over F?
I'll assume you want n to be a positive integer. Consider F[a], the field obtained by adjoining a. Then a^n is in F[a] and the index of F[a] over F is finite. But every element of a field of finite index over F will be algebraic over F.
