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Fields & Galois Theory

e-books in Fields & Galois Theory category

Book cover: Galois Theory: Lectures Delivered at the University of Notre DameGalois Theory: Lectures Delivered at the University of Notre Dame
by - 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.
(347 views)
Book cover: Geometry of the QuinticGeometry of the Quintic
by - 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 ...
(4191 views)

Book cover: The Elements of the Theory of Algebraic NumbersThe Elements of the Theory of Algebraic Numbers
by - 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.
(4140 views)
Book cover: Notes on Galois TheoryNotes on Galois Theory
by - 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.
(3128 views)
Book cover: Lectures On Galois Cohomology of Classical GroupsLectures On Galois Cohomology of Classical Groups
by - Tata Institute of Fundamental Research ,
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.
(4351 views)
Book cover: Algebraic EquationsAlgebraic Equations
by - 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.
(4497 views)
Book cover: Lectures on Field Theory and Ramification TheoryLectures on Field Theory and Ramification Theory
by - Indian Institute of Technology, Bombay ,
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.
(4661 views)
Book cover: Lectures on the Algebraic Theory of FieldsLectures on the Algebraic Theory of Fields
by - 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.
(5532 views)
Book cover: Class Field TheoryClass Field Theory
by ,
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.
(5541 views)
Book cover: Fields and Galois TheoryFields and Galois Theory
by ,
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.
(6121 views)
Book cover: Galois TheoryGalois Theory
by - Macquarie University ,
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.
(8318 views)
Book cover: Galois TheoryGalois Theory
by - 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.
(9352 views)
Book cover: Generic Polynomials: Constructive Aspects of the Inverse Galois ProblemGeneric Polynomials: Constructive Aspects of the Inverse Galois Problem
by - 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.
(9615 views)