A Term of Commutative Algebra
نویسنده
چکیده
Preface . . . . . . . . . . . . . . . . . . . . . . . iii 1. Rings and Ideals . . . . . . . . . . . . . . . . . . . 1 2. Prime Ideals . . . . . . . . . . . . . . . . . . . . 6 3. Radicals . . . . . . . . . . . . . . . . . . . . . . 10 4. Modules . . . . . . . . . . . . . . . . . . . . . . 14 5. Exact Sequences . . . . . . . . . . . . . . . . . . . 20 6. Direct Limits . . . . . . . . . . . . . . . . . . . . 26 7. Filtered Direct Limits . . . . . . . . . . . . . . . . . 33 8. Tensor Products . . . . . . . . . . . . . . . . . . . 37 9. Flatness . . . . . . . . . . . . . . . . . . . . . . 43 10. Cayley–Hamilton Theorem . . . . . . . . . . . . . . . 49 11. Localization of Rings . . . . . . . . . . . . . . . . . 55 12. Localization of Modules . . . . . . . . . . . . . . . . 61 13. Support . . . . . . . . . . . . . . . . . . . . . 66 14. Krull–Cohen–Seidenberg Theory . . . . . . . . . . . . . 71 15. Noether Normalization . . . . . . . . . . . . . . . . 75 Appendix: Jacobson Rings . . . . . . . . . . . . . . . 80 16. Chain Conditions . . . . . . . . . . . . . . . . . . 82 17. Associated Primes . . . . . . . . . . . . . . . . . . 87 18. Primary Decomposition . . . . . . . . . . . . . . . . 91 19. Length . . . . . . . . . . . . . . . . . . . . . . 97 20. Hilbert Functions . . . . . . . . . . . . . . . . . . 101 Appendix: Homogeneity . . . . . . . . . . . . . . . . 107 21. Dimension . . . . . . . . . . . . . . . . . . . . 109 22. Completion . . . . . . . . . . . . . . . . . . . . 115 23. Discrete Valuation Rings . . . . . . . . . . . . . . . 122 24. Dedekind Domains . . . . . . . . . . . . . . . . . 127 25. Fractional Ideals . . . . . . . . . . . . . . . . . . 131 26. Arbitrary Valuation Rings . . . . . . . . . . . . . . . 136 Solutions . . . . . . . . . . . . . . . . . . . . . . 141 1. Rings and Ideals . . . . . . . . . . . . . . . . . 141 2. Prime Ideals . . . . . . . . . . . . . . . . . . 143 3. Radicals . . . . . . . . . . . . . . . . . . . . 145 4. Modules . . . . . . . . . . . . . . . . . . . . 148 5. Exact Sequences . . . . . . . . . . . . . . . . . 149
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تاریخ انتشار 2012