Lecture Notes On Local Rings
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| Title: | Lecture Notes On Local Rings |
|---|---|
| Description: | The content in Chapter 1-3 is a fairly standard one-semester course on local rings with the goal to reach the fact that a regular local ring is a unique factorization domain. The homological machinery is also supported by Cohen-Macaulay rings and depth. In Chapters 4-6 the methods of injective modules, Matlis duality and local cohomology are discussed. Chapters 7-9 are not so standard and introduce the reader to the generalizations of modules to complexes of modules. Some of Professor Iversen's results are given in Chapter 9. Chapter 10 is about Serre's intersection conjecture. The graded case is fully exposed. The last chapter introduces the reader to Fitting ideals and McRae invariants. |
| Authors: | Birger Iversen, Holger Andreas Nielsen |
| Resource Type: | eBook. |
| Subjects: | Local rings, Injective modules (Algebra), Intersection homology theory |
| Categories: | MATHEMATICS / Algebra / General, MATHEMATICS / Geometry / Algebraic, MATHEMATICS / Number Theory |
| Database: | eBook Collection (EBSCOhost) |
| Abstract: | The content in Chapter 1-3 is a fairly standard one-semester course on local rings with the goal to reach the fact that a regular local ring is a unique factorization domain. The homological machinery is also supported by Cohen-Macaulay rings and depth. In Chapters 4-6 the methods of injective modules, Matlis duality and local cohomology are discussed. Chapters 7-9 are not so standard and introduce the reader to the generalizations of modules to complexes of modules. Some of Professor Iversen's results are given in Chapter 9. Chapter 10 is about Serre's intersection conjecture. The graded case is fully exposed. The last chapter introduces the reader to Fitting ideals and McRae invariants. |
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| ISBN: | 9789814603652 9789814603669 9789814603676 |
