Joseph Rotman

Galois Theory (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer US
• Seitenzahl: 176
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9781461206170
• Artikelnr.: 44062757

Inhaltsangabe

From the contents:
- 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
- Appendix A: Group Theory Dictionary
- Appendix B: Group Theory Used in the Text
- Appendix C: Ruler-Compass Constructions
- Appendix D: Old-fashioned Galois Theory
- References. Index