Abstract Algebra: Theory and Applications · Problem 21.5.28

Finite Fields — Thomas Judson

Mathematics — Abstract Algebra · degree-of-simple-extension

Problem

Let

\alpha

be a root of an irreducible monic polynomial

p(x) \in F[x]

, with

\deg p = n

. Prove that

[F(\alpha) : F] = n

. Hint. See the comments following Theorem 21.1.13.