Book:Seth Warner/Modern Algebra
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Seth Warner: Modern Algebra
Published $\text {1965}$, Dover Publications, Inc.
- ISBN 0-486-66341-8
Subject Matter
Contents
- Preface
- CHAPTER $\text {I}$. 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 Structures
- 7. Semigroups and Groups
- CHAPTER $\text {II}$. NEW STRUCTURES FROM OLD
- CHAPTER $\text {III}$. THE NATURAL NUMBERS
- 14. Orderings
- 15. Ordered Semigroups
- 16. The Natural Numbers
- 17. Finite Sets
- 18. Induced $N$-ary Operations
- 19. Combinatorial Analysis
- CHAPTER $\text {IV}$. 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 $\text {V}$. 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 $\text {VI}$. 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 $\text {VII}$. 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 $\text {VIII}$. 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 $\text {IX}$. LINEAR OPERATORS
- 54. Diagonalizable Operators
- 55. Primary and Torsion-free Modules
- 56. Finitely Generated Modules
- 57. Decompositions of Linear Operators
- 58. Determinants
- CHAPTER $\text {X}$. INNER PRODUCT SPACES
- 59. Inner Products
- 60. Orthonormal Bases
- 61. Adjoints
- 62. The Spectral Theorem
- 63. Linear Operators on Inner Product Spaces
- CHAPTER $\text {XI}$. 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)
Click here for errata
Critical View
Thorough, but many of the exercises are busy-work, and hence are not documented on $\mathsf{Pr} \infty \mathsf{fWiki}$.
Source work progress
- Second pass completed up to here
- 1965: Seth Warner: Modern Algebra ... (previous): Chapter $\text {V}$: Vector Spaces: $\S 30$. Linear Equations
- Missing result just before this:
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {V}$: Vector Spaces: $\S 29$. Matrices
- Don't forget this:
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {V}$: Vector Spaces: $\S 29$. Matrices
- Revisit this section:
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {V}$: Vector Spaces: $\S 28$. Linear Transformations: Theorem $28.10$
- Filling out exercises and examples (the worthwhile ones -- plenty are just makework):
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {III}$: The Natural Numbers: $\S 16$: The Natural Numbers: Exercise $16.6 \ \text {(b)}$
- These need completing:
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {III}$: The Natural Numbers: $\S 16$: The Natural Numbers: Exercise $16.28 \ \text {(b)}$
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {III}$: The Natural Numbers: $\S 16$: The Natural Numbers: Exercise $16.27 \ \text {(c)}$
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {III}$: The Natural Numbers: $\S 16$: The Natural Numbers: Exercise $16.26 \ \text {(c)}$
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {III}$: The Natural Numbers: $\S 15$: Ordered Semigroups: Exercise $15.9$
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {III}$: The Natural Numbers: $\S 14$: Orderings: Exercise $14.19 \ \text{(c)}$
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {III}$: The Natural Numbers: $\S 14$: Orderings: Exercise $14.15$
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {III}$: The Natural Numbers: $\S 14$: Orderings: Exercise $14.5$
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {II}$: New Structures from Old: $\S 13$: Compositions Induced on Cartesian Products and Function Spaces: Exercise $13.18$
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {II}$: New Structures from Old: $\S 13$: Compositions Induced on Cartesian Products and Function Spaces: Exercise $13.16$
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {II}$: New Structures from Old: $\S 13$: Compositions Induced on Cartesian Products and Function Spaces: Exercise $13.14 \ \text{(b)}$
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {II}$: New Structures from Old: $\S 13$: Compositions Induced on Cartesian Products and Function Spaces: Exercise $13.9 \ \text{(b)}$
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {II}$: New Structures from Old: $\S 12$: Homomorphisms: Exercise $12.17 \ \text {(a)}$ and a number of others in this section
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {II}$: New Structures from Old: $\S 11$: Quotient Structures: Exercise $11.18 \ \text {(b)}$
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {II}$: New Structures from Old: $\S 11$: Quotient Structures: Exercise $11.18 \ \text {(a)}$
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {II}$: New Structures from Old: $\S 11$: Quotient Structures: Exercise $11.17 \ \text {(a)}$
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {II}$: New Structures from Old: $\S 11$: Quotient Structures: Exercise $11.16$
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {II}$: New Structures from Old: $\S 11$: Quotient Structures: Exercise $11.12$
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {II}$: New Structures from Old: $\S 8$: Compositions Induced on Subsets: Exercise $8.14 \ \text{(b)}$ etc.