Book:C.R.J. Clapham/Introduction to Abstract Algebra

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C.R.J. Clapham: Introduction to Abstract Algebra

Published $1969$, Routledge & Kegan Paul

ISBN 0 7100 6626 0.


Subject Matter


Contents

Preface
1. Integral Domains
1. Introduction
2. Operations
3. Definition of an Integral Domain
4. Elementary Properties
5. Further Examples of Integral Domains
6. The Residue Classes
2. Ordered and Well-Ordered Integral Domains
7. Order
8. Well-Order
3. The Integers
9. The Principles of Induction
10. Divisibility
11. Highest Common Factor
12. Primes
13. Unique Factorisation
4. Fields
14. Definition of a Field
15. Examples of Fields
16. Subfields
17. The Characteristic of a Field
5. Rings
18. Definition of a Ring
19. Subrings
20. Cosets
21. Ideals
22. Quotient Rings
23. Maximal Ideals
24. Homomorphisms
6. Polynomials and Euclidean Rings
25. Polynomials
26. Divisibility
27. Euclidean Rings
28. Highest Common Factor
29. Irreducible Elements
30. Unique Factorisation
31. Polynomials with Integer Coefficients
7. Vector Spaces
32. Definition of a Vector Space
33. Definition of a Basis
34. Dimension
35. Coordinates
8. Field Extensions
36. The Degree of a Field Extension
37. Roots of a Polynomial
38. Simple Algebraic Extensions
39. A More Sophisticated Approach
40. Constructions with Ruler and Compasses
Exercises
Answers to the Exercises
Index