
Fundamental Concepts of Algebra
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Content
- Front Cover
- Fundamental Concepts of Algebra
- Copyright Page
- Contents
- Preface
- Prerequisite knowledge and terminological conventions
- Chapter I. Monoids
- 1. Definition of a monoid
- 2. Submonoids. Generators
- 3. Homomorphisms
- 4. Quotient monoids
- 5. Products
- 6. Free monoids
- Exercises
- Chapter II. Groups
- 1. Definition of a group
- 2. Subgroups
- 3. Homomorphisms. Quotient groups
- 4. Groups operating on a set
- 5.Products of groups
- 6. Free groups
- Exercises
- Chapter III. Rings and modules
- 1. Rings
- 2. Field of quotients
- 3. Modules
- 4. Submodules
- 5. Linear mappings
- 6. Products
- 7. Uniqueness theorems for semi-simple modules
- 8. Tensor products of modules
- 9. Free modules. Bases
- 10. Multilinear mappings
- 11. Transfer of basic rings
- 12. Vector spaces
- 13. Vector spaces in duality
- 14. The rank of a linear mapping
- 15. Matrices
- 16. Systems of linear equations
- 17. Graded modules
- Exercises
- Chapter IV. Algebras
- 1. Definition
- 2. Subalgebras
- 3. Homomorphisms
- 4. Products
- 5. Free algebra
- Exercises
- Chapter V. Associative algebras
- 1. Definitions
- 2. Graded algebras
- 3. Tensor algebras
- 4. Tensor products of graded algebras
- 5. Anticommutative algebras
- 6. Derivations
- 7. Exterior algebras
- 8. Grassmann algebras
- 9. The determinant of a matrix
- 10. Some applications of determinants
- 11. Existence of certain derivations
- 12. The trace of a matrix
- 13. Alternating multilinear mappings
- 14. The Pfaffian of an alternating bilinear form
- 15. Exterior algebras on vector spaces
- 16. Transfer of the basic ring
- 17. Commutative tensor products
- 18. Symmetric algebras
- 19. Polynomial algebras
- Exercises
- Index
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