ProofWiki:Books/Seth Warner/Modern Algebra
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Seth Warner: Modern Algebra
Published 1965, Dover Publications, Inc..
ISBN 0-486-66341-8
Subject Matter
Contents
- Preface
- CHAPTER I. ALGEBRAIC STRUCTURES
- 1. The Language of Set Theory
- 2. Compositions
- 3. Unions and Intersections of Sets
- 4. Neutral Elements and Inverses
- 5. Compositions and Inverses of Functions
- 6. Isomorphisms of Algebraic Structure
- 7. Semigroups and Groups
- CHAPTER II. NEW STRUCTURES FROM OLD
- 8. Compositions Induced on Subsets
- 9. Compositions Induced on the Set of All Subsets
- 10. Equivalence Relations
- 11. Quotient Structures
- 12. Homomorphisms
- 13. Compositions Induced on Cartesian Products and Function Spaces
- CHAPTER III. THE NATURAL NUMBERS
- 14. Orderings
- 15. Ordered Semigroups
- 16. The Natural Numbers
- 17. Finite Sets
- 18. Induced $N$-ary Operations
- 19. Combinatorial Analysis
- CHAPTER IV. RINGS AND FIELDS
- 20. The Integers
- 21. Rings and Integral Domains
- 22. New Rings from Old
- 23. The Field of Rational Numbers
- 24. The Division Algorithm
- 25. Cyclic Groups and Lagrange's Theorem
- CHAPTER V. VECTOR SPACES
- 26. Vector Spaces and Modules
- 27. Subspaces and Bases
- 28. Linear Transformations
- 29. Matrices
- 30. Linear Equations
- 31. Direct Sums and Quotient Spaces
- 32. Rings of Linear Operators
- CHAPTER VI. POLYNOMIALS
- 33. Algebras
- 34. The Algebra of Polynomials
- 35. Principal Ideal Domains
- 36. Substitution
- 37. Irreducibility Criteria
- 38. Adjoining Roots
- 39. Finite Fields and Division Rings
- 40. Polynomials in Several Indeterminates
- CHAPTER VII. THE REAL AND COMPLEX NUMBER FIELDS
- 41. Dedekind and Archimedean Ordered Fields
- 42. The Construction of a Dedekind Ordered Field
- 43. Isomorphisms of Archimedean Ordered Groups
- 44. The Field of Complex Numbers
- 45. The Algebra of Quaternions
- CHAPTER VIII. ALGEBRAIC EXTENSIONS OF FIELDS
- 46. Algebraic Extensions
- 47. Constructions by Ruler and Compass
- 48. Galois Theory
- 49. Separable and Normal Extensions
- 50. Roots of Unity
- 51. Solving Quadratics, Cubics, and Quartics
- 52. Permutation Groups
- 53. Solving Polynomials by Radicals
- CHAPTER IX. LINEAR OPERATORS
- 54. Diagonalizable Operators
- 55. Primary and Torsion-free Modules
- 56. Finitely Generated Modules
- 57. Decompositions of linear Operators
- 58. Determinants
- CHAPTER X. INNER PRODUCT SPACES
- 59. Inner Products
- 60. Orthonormal Bases
- 61. Adjoints
- 62. The Spectral Theorem
- 63. Linear Operators on Inner Product Spaces
- CHAPTER XI. THE AXIOM OF CHOICE
- 64. The Axiom of Choice
- 65. Zorn's Lemma
- 66. Algebraic Closures
- LIST OF SYMBOLS (PAGES 1-457)
- LIST OF SYMBOLS (PAGES 459-797)
- INDEX (PAGES 1-457)
- INDEX (PAGES 459-797)
