3. Prime Ideals and Maximal Ideals

Chapters in this book

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