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 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 Emil Artin - University of Notre Dame
The book deals with linear algebra, including fields, vector spaces, homogeneous linear equations, and determinants, extension fields, polynomials, algebraic elements, splitting fields, group characters, normal extensions, roots of unity, and more.
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.
by C. U. Jensen, A. Ledet, N. Yui - Cambridge University Press
A clearly written book, which uses exclusively algebraic language (and no cohomology), and which will be useful for every algebraist or number theorist. It is easily accessible and suitable also for first-year graduate students.