Desvl's blog

A Separable Extension Is Solvable by Radicals Iff It Is Solvable

We show that a separable extension is solvable by radical iff it is solvable, i.e. it has a Galois closure with solvable Galois group. The proof is done in a general setting.

Examples in Galois Theory 2 - Cubic Extensions

We study the Galois group of a cubic polynomial over a field with characteristic not equal to 2 and 3.

Examples in Galois Theory 1 - Complex Field is Algebraically Closed

We try to prove the fundamental theorem of algebra, that the complex field is algebraically closed, using as little analysis as possible. In other words, the following proof will be *almost* algebraic.