Iain T. Adamson

An Introduction to Field Theory

• Broschiertes Buch

Produktbeschreibung

This book brings the reader from the basic definitions to important results and applications, and introduces some of the techniques of abstract algebra.

Produktdetails

• Verlag: Cambridge University Press
• Revised
• Seitenzahl: 192
• Erscheinungstermin: 26. August 2008
• Englisch
• Abmessung: 203mm x 127mm x 11mm
• Gewicht: 213g
• ISBN-13: 9780521286589
• ISBN-10: 0521286581
• Artikelnr.: 25586884

Inhaltsangabe

Preface
Part I: Elementary Definitions
1. Rings and fields
2. Elementary properties
3. Homomorphisms
4. Vector spaces
5. Polynomials
6. Higher polynomial rings
rational functions
Part II: Extensions of fields
7. Elementary properties
8. Simple extensions
9. Algebraic extensions
10. Factorisation of polynomials
11. Splitting fields
12. Algebraically closed fields
13. Separable extensions
Part III: Galois theory
14. Automorphisms of fields
15. Normal extensions
16. The fundamental theorem of Galois Theory
17. Norms and traces
18. The primitive element theorem
Lagrange's theorem
19. Normal bases
Part IV: Applications
20. Finite fields
21. Cyclotomic extensions
22. Cyclotomic extensions of the rational number field
23. Cyclic extensions
24. Wedderburns' theorem
25. Ruler-an-compasses constructions
26. Solution by radicals
27. Generic polynomials.