Fields and Galois Theory
by J. S. Milne
2008
Number of pages: 111
Description:
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.
Download or read it online for free here:
Download link
(940KB, PDF)
Similar books
The Elements of the Theory of Algebraic Numbersby Legh Wilber Reid - The Macmillan company
It has been my endeavor in this book to lead by easy stages a reader, entirely unacquainted with the subject, to an appreciation of some of the fundamental conceptions in the general theory of algebraic numbers. Many numerical examples are given.
(9837 views)
Galois Theoryby 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.
(16028 views)
Generic Polynomials: Constructive Aspects of the Inverse Galois Problemby 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.
(15593 views)
Class Field Theoryby 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.
(11491 views)