Elementary Abstract Algebra

Description

Title Preface Contents I. Binary operations §1. Introduction §2. Notations and terminology from set theory §3. Binary operations on a set §4. Equivalence relations §5. Stability of an equivalence relation with respect to a binary operation §6. Commutative binary operations §7. Associative binary operations §8. Identity elements §9. Inverse elements §10. The distributive laws §11. Additive and multiplicative notations II. Groups §12. Introduction §13. Semi-groups §14. Groups §15. Permutations §16. Subgroups §17. Normal subgroups §18. Factor groups §19. Isomorphism §20. Homomorphism III. Rings, integral domains and fields §21. Introduction §22. Rings §23. Matrices §24. Fields §25. Integral domains §26. Isomorphism and homomorphism of rings §27. The field of rational numbers §28. The field of complex numbers §29. The ring of residue classes mod n §30. Subrings §31. The characteristic of an integral domain §32. Ideals and factor rings IV. Polynomial and Euclidean rings §33. Introduction §34. Polynomials in a single indeterminate §35. Polynomial rings §36. Power series §37. Euclidean rings §38. Prime factorisation in Euclidean rings §39. Residue class rings §40. Algebraic extensions of a field §41. Algebraically closed fields §42. Roots of polynomials V. Vector spaces §43. Introduction §44. Geometrical vectors §45. Addition of geometrical vectors §46. Vector spaces §47. Linear dependence and dimension §48. Subspaces and direct sums §49. Unitary spaces §50. Normed vector spaces §51. Linear algebras §52. Lie algebras Solutions to exercises Index