The book discusses classical 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 discusses algebraic closure andinfinite Galois extensions, and concludes with a new chapter on transcendental extensions. Key topics and features of this second edition: (1) Approaches Galois theory from the linear algebra point of view, following Artin; (2) 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. Concise and clear treatment of the subject Stresseslinear algebra approach Presents further topics in field theory Second edition includes expanded key chapter on transcendental extensions Better format andlayout INDICE: Introduction 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.- Transcendental Extensions.- A.Some Results from Group Theory.- B. A Lemma on Constructing Fields.- C. A Lemma from Elementary Number Theory.- References.- Index.
- ISBN: 978-0-387-87574-3
- Editorial: Springer
- Encuadernacion: Rústica
- Páginas: 225
- Fecha Publicación: 01/12/2008
- Nº Volúmenes: 1
- Idioma: Inglés
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- MATEMÁTICAS /
- ÁLGEBRA