Conversion of Galios Group Into Algebraic Form

Question

Suppose L: K is a Galios extension whose Galios group G is isomorphic to the Klein four group. Assume that K does not have characteristic 2. Show that there exists x, y ε k such that every element of L can be expressed in the form a + b√x + c√y + d√xy with a, b, c, d, ε K.

Summary

The question belongs to Mathematics and it is about calculation of Galios group isomorphic to Klein four group can be expressed in algebraic form.

Note: The solution is in handwritten format.

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    Giuseppe

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