Introducción a la teoría de valoraciones

Abstract

This paper makes an introduction to the theory of valuations on fields, we try to analyse the extension of valuations in transcendental extensions and the application on the irreducibility of polynomials showing the criterion of irreducibility of Eisenstein and noting that other many criteria of irreducibility of polynomials can be demonstrated through this theory. In this work we have relied on the work already done by Michel VAQUIÉ in Valuations (August 17, 1998) and by Saunders MacLane in A construction for absolute values in polynomial rings (1936).