Galois Theory
1st Edition
Will be published approx. on 6. December 1994
Book
Paperback/Softback
XII, 108 pages
978-0-387-97305-0 (ISBN)
Description
This text offers a clear, efficient exposition of Galois Theory with exercises and complete proofs. Topics include: Cardano's formulas; the Fundamental Theorem; Galois' Great Theorem (solvability for radicals of a polynomial is equivalent to solvability of its Galois Group); and computation of Galois group of cubics and quartics. There are appendices on group theory and on ruler-compass constructions. Developed on the basis of a second-semester graduate algebra course, following a course on group theory, this book will provide a concise introduction to Galois Theory suitable for graduate students, either as a text for a course or for study outside the classroom.
More details
Series
Language
English
Place of publication
New York
United States
Target group
Primary & secondary/elementary & high school
Graduate
Illustrations
XII, 108 p.
Dimensions
Height: 23.5 cm
Width: 15.5 cm
Weight
454 gr
ISBN-13
978-0-387-97305-0 (9780387973050)
DOI
10.1007/978-1-4684-0367-1
Schweitzer Classification
Other editions
New editions
Content
Rings.- Homomorphisms and Ideals.- Quotient Rings.- Polynomial Rings over Fields.- Prime Ideals and Maximal Ideals.- Finite Fields.- Irreducible Polynomials.- Classical Formulas.- Splitting Fields.- Solvability by Radicals.- The Galois Group.- Primitive Roots of Unity.- Insolvability of the Quintic.- Independence of Characters.- Galois Extensions.- Fundamental Theorem of Galois Theory.- Applications.- Galois's Great Theorem.- Discriminants.- Galois Groups of Quadratics, Cubics, and Quartics.- Epilogue.- Appendix 1. Group Theory Dictionary.- Appendix 2. Group Theory Used in the Text.- Appendix 3. Ruler-Compass Constructions.- Appendix 4. Old-fashioned Galois Theory.- References.