Book:C.R.J. Clapham/Introduction to Abstract Algebra
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C.R.J. Clapham: Introduction to Abstract Algebra
Published $\text {1969}$, 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
Source work progress
- 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous): Exercises: Chapter $1$: Exercise $1 \ \text{(iv)}$
- Section $39$ has been omitted as it is a discursion with an imprecise structure.
- The bulk of the exercises (all collected at the end) remain to be documented.