Field Extensions and Galois Theory [Paperback]

This 1984 book makes the general theory of field extensions accessible to any reader with a modest background in groups, rings and vector spaces.This 1984 book aims to make the general theory of field extensions accessible to any reader with a modest background in groups, rings and vector spaces. Galois theory is regarded amongst the central and most beautiful parts of algebra and its creation marked the culmination of generations of investigation.This 1984 book aims to make the general theory of field extensions accessible to any reader with a modest background in groups, rings and vector spaces. Galois theory is regarded amongst the central and most beautiful parts of algebra and its creation marked the culmination of generations of investigation.Originally published in 1984, the principal objective of this book is to make the general theory of field extensions accessible to any reader with a modest background in groups, rings and vector spaces. Galois theory is generally regarded as one of the central and most beautiful parts of algebra and its creation marked the culmination of investigations by generations of mathematicians on one of the oldest problems in algebra, the solvability of polynomial equations by radicals.Editor's statement; Section editor's foreword; Preface; Historical introduction; Prerequisites; Notation; 1. Preliminaries on fields and polynomials; 2. Algebraic extensions; 3. Galois theory; 4. Transcendental Extensions; References and selected bibliography; Index.