Abstract Algebra: Theory and Applications · Problem 21.5.21

Finite Fields — Thomas Judson

Mathematics — Abstract Algebra · automorphism-permutes-zeros

Problem

Let EE be an algebraic extension of a field FF, and let σ\sigma be an automorphism of EE leaving FF fixed. Let α∈E\alpha \in E. Show that σ\sigma induces a permutation of the set of all zeros of the minimal polynomial of α\alpha that are in EE.

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