Preface to the second edition Preface to the first edition Glossary of symbols Part I. Preliminaries: 1. Sets and mappings 2. Integers, real numbers, and complex numbers 3. Matrices and determinants Part II. Groups: 4. Groups 5. Normal subgroups 6. Normal series 7. Permutation groups 8. Structure theorems of groups Part III. Rings and Modules: 9. Rings 10. Ideals and homomorphisms 11. Unique factorization domains and euclidean domains 12. Rings of fractions 13. Integers 14. Modules and vector spaces Part IV. Field Theory: 15. Algebraic extensions of fields 16. Normal and separable extensions 17. Galois theory 18. Applications of Galios theory to classical problems Part V. Additional Topics: 19. Noetherian and Artinian modules and rings 20. Smith normal form over a PID and rank 21. Finitely generated modules over a PID 22. Tensor products Solutions to odd-numbered problems Selected bibliography Index.
Preface to the second edition Preface to the first edition Glossary of symbols Part I. Preliminaries: 1. Sets and mappings 2. Integers, real numbers, and complex numbers 3. Matrices and determinants Part II. Groups: 4. Groups 5. Normal subgroups 6. Normal series 7. Permutation groups 8. Structure theorems of groups Part III. Rings and Modules: 9. Rings 10. Ideals and homomorphisms 11. Unique factorization domains and euclidean domains 12. Rings of fractions 13. Integers 14. Modules and vector spaces Part IV. Field Theory: 15. Algebraic extensions of fields 16. Normal and separable extensions 17. Galois theory 18. Applications of Galios theory to classical problems Part V. Additional Topics: 19. Noetherian and Artinian modules and rings 20. Smith normal form over a PID and rank 21. Finitely generated modules over a PID 22. Tensor products Solutions to odd-numbered problems Selected bibliography Index.
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