| Description |
xvi, 785 pages : illustrations ; 24 cm |
| Series |
Graduate texts in mathematics ; 150 |
|
Graduate texts in mathematics ; 150
|
| Contents |
1. Roots of Commutative Algebra -- 2. Localization -- 3. Associated Primes and Primary Decomposition -- 4. Integral Dependence and the Nullstellensatz -- 5. Filtrations and the Artin-Rees Lemma -- 6. Flat Families -- 7. Completions and Hensel's Lemma -- 8. Introduction to Dimension Theory -- 9. Fundamental Definitions of Dimension Theory -- 10. The Principal Ideal Theorem and Systems of Parameters -- 11. Dimension and Codimension One -- 12. Dimension and Hilbert-Samuel Polynomials -- 13. The Dimension of Affine Rings -- 14. Elimination Theory, Generic Freeness, and the Dimension of Fibers -- 15. Grobner Bases -- 16. Modules of Differentials -- 17. Regular Sequences and the Koszul Complex -- 18. Depth, Codimension, and Cohen-Macaulay Rings -- 19. Homological Theory of Regular Local Rings -- 20. Free Resolutions and Fitting Invariants -- 21. Duality, Canonical Modules, and Gorenstein Rings -- Appendix 1 Field Theory -- Appendix 2 Multilinear Algebra |
|
Appendix 3 Homological Algebra -- Appendix 4 A Sketch of Local Cohomology -- Appendix 5 Category Theory -- Appendix 6 Limits and Colimits |
| Analysis |
Algebra |
| Bibliography |
Includes bibliographical references and index |
| Subject |
Commutative algebra.
|
|
Geometry, Algebraic.
|
|
Commutative algebra.
|
|
Geometry, Algebraic.
|
| LC no. |
94017351 |
| ISBN |
0387942688 (hard cover) |
|
0387942696 (soft cover) |
|
