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Fields & Galois Theory
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e-books in this category
The Elements of the Theory of Algebraic Numbers
by Legh Wilber Reid - The Macmillan company , 1910
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.
Notes on Galois Theory
by Mark Reeder - Boston College , 2012
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.
Lectures On Galois Cohomology of Classical Groups
by M. Kneser - Tata Institute of Fundamental Research , 1969
The main result is the Hasse principle for the one-dimensional Galois cohomology of simply connected classical groups over number fields. For most groups, this result is closely related to other types of Hasse principle.
by George Ballard Mathews - Cambridge University Press , 1907
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.
Lectures on Field Theory and Ramification Theory
by Sudhir R. Ghorpade - Indian Institute of Technology, Bombay , 2008
These are notes of a series of lectures, aimed at covering the essentials of Field Theory and Ramification Theory as may be needed for local and global class field theory. Included are the two sections on cyclic extensions and abelian extensions.
Lectures on the Algebraic Theory of Fields
by K.G. Ramanathan - Tata Institute of Fundamental Research , 1956
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.
Class Field Theory
by J. S. Milne , 2008
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.
Fields and Galois Theory
by J. S. Milne , 2008
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; The fundamental theorem of Galois theory; etc.
by Christopher Cooper - Macquarie University , 2009
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. There is a chapter that gives a proof of the Fundamental Theorem of Algebra.
by Miles Reid - University of Warwick , 2004
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.
Generic Polynomials: Constructive Aspects of the Inverse Galois Problem
by C. U. Jensen, A. Ledet, N. Yui - Cambridge University Press , 2002
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.