Fields and Galois Theory
by J. S. Milne
Number of pages: 111
A concise treatment of Galois theory and the theory of fields, including transcendence degrees and infinite Galois extensions. Contents: Basic definitions and results. Splitting fields; multiple roots. The fundamental theorem of Galois theory. Computing Galois groups. Applications of Galois theory. Algebraic closures. Infinite Galois theory. Transcendental Extensions.
Home page url
Download or read it online for free here:
by J. S. Milne
Class field theory describes the abelian extensions of a local or global field in terms of the arithmetic of the field itself. These notes contain an exposition of abelian class field theory using the algebraic/cohomological approach.
by K.G. Ramanathan - Tata Institute of Fundamental Research
These lecture notes on Field theory are aimed at providing the beginner with an introduction to algebraic extensions, algebraic function fields, formally real fields and valuated fields. We assume a familiarity with group theory and vector spaces.
by George Ballard Mathews - Cambridge University Press
This book is intended to give an account of the theory of equations according to the ideas of Galois. This method analyzes, so far as exact algebraical processes permit, the set of roots possessed by any given numerical equation.
by Miles Reid - University of Warwick
The author discusses the problem of solutions of polynomial equations both in explicit terms and in terms of abstract algebraic structures. The course demonstrates the tools of abstract algebra as applied to a meaningful problem.