Wow! eBook
Lecture Notes On Local Rings
Author(s): Birger Iversen (Author), Holger Andreas Nielsen
- Publisher: Wspc
- Publication Date: 20 Jun. 2014
- Edition: 1st
- Language: English
- Print length: 224 pages
- ISBN-10: 9814603651
- ISBN-13: 9789814603652
Book Description
This is a very nice text on some important topics on commutative ring theory. Mathematical Association of America The content in Chapter 13 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 CohenMacaulay rings and depth. In Chapters 46 the methods of injective modules, Matlis duality and local cohomology are discussed. Chapters 79 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.
Editorial Reviews
Review
This is a very nice text on some important topics on commutative ring theory. —Mathematical Association of America
When it comes to applications in commutative algebra of the homological theory of complexes, Iversen was one of the pioneers and, as was noted above, the book even includes some of his original work in that area. It is still an active area of research, and a little patience may be required to reconcile the book’s terminology with that of contemporary research articles. This book is for those who prefer — or at least want to experiment with — the alternative: using a lean text to which the lecturer has to add supplementary material. This reviewer does not know of any such text that like this one, emphasizes the homological approach to local algebra. —
Mathematical Reviews
