Carefully state the following theorems you do not need to pr

Carefully state the following theorems (you do not need to prove them): Theorem relating the image of a epsilon E under an element of Gal(E/F) to the minimal polynomial irr(alpha, F). Theorem concerning separability of F rightarrow E when F is finite or has characteristic zero. Fundamental theorem of Galois theory. Galois\' criterion for solvability by radicals.

Solution

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In mathematics, more specifically in the area of modern algebra known as Galois theory, the Galois group of a certain type of field extension is a specific groupassociated with the field extension. The study of field extensions and their relationship to the polynomials that give rise to them via Galois groups is calledGalois theory, so named in honor of Évariste Galois who first discovered them.

For a more elementary discussion of Galois groups in terms of permutation groups, see the article on Galois theorm