Fields & Galois Theory

e-books in Fields & Galois Theory category

Galois Theory: Lectures Delivered at the University of Notre Dame
by Emil Artin - University of Notre Dame , 1971
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.
(6003 views)

Geometry of the Quintic
by Jerry Shurman - Wiley-Interscience , 1997
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 ...
(10966 views)

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.
(9904 views)

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.
(9376 views)

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.
(9954 views)

Algebraic Equations
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.
(10644 views)

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.
(10506 views)

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.
(11023 views)

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.
(11584 views)

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.
(12435 views)

Galois Theory
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.
(16134 views)

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.
(15685 views)