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.

In this post we study cyclotomic polynomials in field theory and deduce some baisc properties of it. We will also use it to solve some problems in field theory.

In this post, we develop a fundamental device: absolute value on an arbitrary field with various points of view.