Galois Theory

ISBN-10: 0387985417

ISBN-13: 9780387985411

Edition: 2nd 1998 (Revised)

Authors: Joseph Rotman
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Description: This text offers a clear, efficient exposition of Galois Theory with complete proofs and exercises. Topics include: cubic and quartic formulas; Fundamental Theory of Galois Theory; insolvability of the quintic; Galois's Great Theorem (solvability by radicals of a polynomial is equivalent to solvability of its Galois Group); and computation of Galois groups of cubics and quartics. There are appendices on group theory, ruler-compass constructions, and the early history of Galois Theory. This book provides a concise introduction to Galois Theory suitable for first-year graduate students, either as a text for a course or for study outside the classroom.This new edition has been completely rewritten in an attempt to make proofs clearer by providing more details. The book now begins with a short section on symmetry groups of polygons in the plane, for there is an analogy between polygons and their symmetry groups and polynomials and their Galois groups; this analogy can serve as a guide by helping readers organize the various field theoretic definitions and constructions. The exposition has been reorganized so that the discussion of solvability by radicals now appears later and several new theorems not found in the first edition are included (e.g., Casus Irreducibilis).

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Book details

List price: $59.95
Edition: 2nd
Copyright year: 1998
Publisher: Springer
Publication date: 7/27/2001
Binding: Paperback
Pages: 176
Size: 6.50" wide x 9.50" long x 0.75" tall
Weight: 0.550
Language: English

Preface to the Second Edition
Preface to the First Edition
To the Reader
Symmetry
Rings
Domains and Fields
Homomorphisms and Ideals
Quotient Rings
Polynomial Rings over Fields
Prime Ideals and Maximal Ideals
Irreducible Polynomials
Classical Formulas
Splitting Fields
The Galois Group
Roots of Unity
Solvability by Radicals
Independence of Characters
Galois Extensions
The Fundamental Theorem of Galois Theory
Applications
Galois's Great Theorem
Discriminants
Galois Groups of Quadratics, Cubics, and Quartics
Epilogue
Group Theory Dictionary
Group Theory Used in the Text
Ruler-Compass Constructions
Old-fashioned Galois Theory
References
Index
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