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14. Dimension
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John J. Watkins
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Chapters in this book
- Frontmatter i
- Contents vii
- Preface ix
- 1. Rings and Subrings 1
- 2. Ideals and Quotient Rings 11
- 3. Prime Ideals and Maximal Ideals 23
- 4. Zorn’s Lemma and Maximal Ideals 35
- 5. Units and Nilpotent Elements 45
- 6. Localization 51
- 7. Rings of Continuous Functions 69
- 8. Homomorphisms and Isomorphisms 80
- 9. Unique Factorization 89
- 10. Euclidean Domains and Principal Ideal Domains 100
- 11. Polynomial Rings 110
- 12. Power Series Rings 119
- 13. Noetherian Rings 128
- 14. Dimension 137
- 15. Gröbner Bases 154
- Solutions to Selected Problems 185
- Suggestions for Further Reading 209
- Index 213
Chapters in this book
- Frontmatter i
- Contents vii
- Preface ix
- 1. Rings and Subrings 1
- 2. Ideals and Quotient Rings 11
- 3. Prime Ideals and Maximal Ideals 23
- 4. Zorn’s Lemma and Maximal Ideals 35
- 5. Units and Nilpotent Elements 45
- 6. Localization 51
- 7. Rings of Continuous Functions 69
- 8. Homomorphisms and Isomorphisms 80
- 9. Unique Factorization 89
- 10. Euclidean Domains and Principal Ideal Domains 100
- 11. Polynomial Rings 110
- 12. Power Series Rings 119
- 13. Noetherian Rings 128
- 14. Dimension 137
- 15. Gröbner Bases 154
- Solutions to Selected Problems 185
- Suggestions for Further Reading 209
- Index 213
