Field extension

Normal extension

A field extension is normal iff every has a root iff it splits into linear factors in . field Equivalently,¹

• Every embedding induces an automorphism of ;

• is the Splitting field of a family of polynomials in .

Proof

proof

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Footnotes

1. 2009. Algebra: Chapter 0, §VII.4.1, p. 431 ↩