Insolubilidad de ecuaciones algebraicas de grado mayor o igual a cinco mediante radicales

Abstract

The Escuela Superior Politécnica de Chimborazo does not have evidence on the existence of bibliographic information about the Galois Theory, applied to the insolubility of algebraic equations with a degree greater than or equal to five by means of radicals, this impedes students interested in the subject to carry out their research. Therefore, the aim of this research is to analyze the Galois theory, through the review of specialized bibliographic material, in order to generate a monograph on the insolubility of algebraic equations with a degree greater than or equal to five by means of radicals, which was developed using the LATEX text editor. The development of this work was based on a qualitative approach, descriptive level and documentary type research. Finally, the result was a monograph entitled: Insolubility of algebraic equations with a degree greater than or equal to five by means of radicals. The monograph has four chapters: the first chapter has to do with the study of rings and fields; the second chapter deals with the rings of polynomials topic; the third chapter studies extensions of fields and the fourth chapter focuses on the Galois theory, where the demonstration of the insolubility of equations with degree greater than or equal to five by means of radicals is covered. Therefore, from the analysis of the theory of rings and field extensions it was possible to determine the demonstration of the insolubility of algebraic equations by means of radicals with a degree greater than or equal to five.