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23.2: The Fundamental Theorem
https://math.libretexts.org/Bookshelves/Abstract_and_Geometric_Algebra/Abstract_Algebra%3A_Theory_and_Applications_(Judson)/23%3A_Galois_Theory/23.02%3A_The_Fundamental_Theorem
If every irreducible polynomial in $F[x]$ with a root in $E$ has all of its roots in $E\text{,}$ then $E$ is called a normal extension of $F\text{;}$ that is, every irreducible polynomial in...If every irreducible polynomial in $F[x]$ with a root in $E$ has all of its roots in $E\text{,}$ then $E$ is called a normal extension of $F\text{;}$ that is, every irreducible polynomial in $F[x]$ containing a root in $E$ is the product of linear factors in $E[x]$ .

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