Galois Theory

Classical Galois theory is a subject generally acknowledged to be one of the most central and beautiful areas in pure mathematics. This text develops the subject systematically and from the beginning, requiring of the reader only basic facts about polynomials and a good knowledge of linear algebra.

Key topics and features of this book:

• Approaches Galois theory from the linear algebra point of view, following Artin

• Develops the basic concepts and theorems of Galois theory, including algebraic, normal, separable, and Galois extensions, and the Fundamental Theorem of Galois Theory

• Presents a number of applications of Galois theory, including symmetric functions, finite fields, cyclotomic fields, algebraic number fields, solvability of equations by radicals, and the impossibility of solution of the three geometric problems of Greek antiquity

• Excellent motivaton and examples throughout

The book discusses Galois theory in considerable generality, treating fields of characteristic zero and of positive characteristic with consideration of both separable and inseparable extensions, but with a particular emphasis on algebraic extensions of the field of rational numbers. While most of the book is concerned with finite extensions, it concludes with a discussion of the algebraic closure and of infinite Galois extensions.

Steven H. Weintraub is Professor and Chair of the Department of Mathematics at Lehigh University. This book, his fifth, grew out of a graduate course he taught at Lehigh. His other books include Algebra: An Approach via Module Theory (with W. A. Adkins).

Texte du rabat

Galois theory is a mature mathematical subject of particular beauty. Any Galois theory book written nowadays bears a great debt to Emil Artin's classic text "Galois Theory," and this book is no exception. While Artin's book pioneered an approach to Galois theory that relies heavily on linear algebra, this book's author takes the linear algebra emphasis even further. This special approach to the subject together with the clarity of its presentation, as well as the choice of topics covered, makes this book a more than worthwhile addition to the existing literature on Galois Theory. It will be appreciated by undergraduate and beginning graduate math majors.

Contenu

to Galois Theory.- Field Theory and Galois Theory.- Development and Applications of Galois Theory.- Extensions of the field of Rational Numbers.- Further Topics in Field Theory.