by Christopher Cooper
Publisher: Macquarie University 2009
Number of pages: 86
This text follows the usual path through to Galois groups, but just for subfields of the complex numbers. It takes as its goal the insolubility of polynomials by radicals. This is as far as we normally reach, though there is an additional chapter that gives an algebraic proof of the Fundamental Theorem of Algebra, using Sylow theory.
Home page url
Download or read it online for free here:
(multiple PDF files)
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 Jerry Shurman - Wiley-Interscience
The text demonstrates the use of general concepts by applying theorems from various areas in the context of one problem -- solving the quintic. This book helps students to develop connections between the algebra, geometry, and analysis ...
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 Mark Reeder - Boston College
From the table of contents: Basic ring theory, polynomial rings; Finite fields; Extensions of rings and fields; Computing Galois groups of polynomials; Galois groups and prime ideals; Cyclotomic extensions and abelian numbers.