An alternative approach to the concept of separability in Galois theory

Abstract

The notion of a separable extension is an important concept in Galois theory. Traditionally, this concept is introduced using the minimal polynomial and the formal derivative. In this work, we present an alternative approach to this classical concept.Based on our approach, we will give new proofs of some basic results about separable extensions (such as the existence of the separable closure, Theorem of the primitive element and the transitivity of separability).