ABSTRACT
In this section we will first derive a complete characterization of algebraic Galois extension. Once this is done we can show that for finite Galois extension the mappings F and G which constitute the Galois correspondence are inverse bijections and hence faithfully relate the field-theoretical structure of (L : K) with the group-theoretical structure of G K L https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315136554/b1e97aa6-f63a-4d22-960d-a98dde0e94f9/content/eq4766.tif"/> ; this is called the Main Theorem of Galois theory. Let us begin by characterizing algebraic Galois extensions.
