Estudo sobre extensões de corpos: justificando impossibilidades de construções com régua e compasso

Abstract

This work aims to conduct a detailed study on the theory of field extensions, seeking tools to algebraically justify the impossibility of performing, with ruler and compass, the constructions involved in the three classical Greek problems: constructing a square with the same area as a given circle, constructing a cube with twice the volume of a given cube, and trisecting a given angle. To this end, we need to explore concepts, propositions, theorems, and related examples concerning the theory of field extensions and ruler-and compass constructions.