Normal Field Extensions

We have seen in previous chapters that - given an algebraic field extension L|K and an algebraic closure \(\Omega\) of L - the set \(\mathrm {Hom}_{K}(L,\Omega )\) plays an important role. We now define normal field extensions L|K which guarantee that \(\mathrm {Hom}_{K}(L,\Omega )=\mathrm {Aut}_{K}(L)\) holds and this is very nice since the right hand side form as group.