Galois Theory - Brossura

Weintraub, Steven H.

Brossura

ISBN 10: 0387287256 ISBN 13: 9780387287256

Casa editrice: Springer Verlag, 2005

Riassunto

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 are: it approaches Galois theory from the linear algebra point of view, following Artin; it develops the basic concepts and theorems of Galois theory, including algebraic, normal, separable, and Galois extensions, and the Fundamental Theorem of Galois Theory; it 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; and, it offers 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).

Su questo libro

Dalla quarta di copertina

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).

Dettagli dell'edizione

• Editore: Springer Verlag
• Data di pubblicazione: 2005
• Lingua: Inglese
• ISBN 10: 0387287256
• ISBN 13: 9780387287256
• Rilegatura: Copertina flessibile
• Numero di pagine: 185
• Contatto del produttore: non disponibile
• Persona responsabile: CMN Printpool Inh. Mathis Neumann; https://www.also.com/ec/cms5/en_6000/6000/index.jsp; ; Friedrich-Karl-Str. 9; Hamburg; Germania