Lecture Notes On Local Rings - Hardcover

Iversen, Birger

Hardcover

ISBN 10: 9814603651 ISBN 13: 9789814603652

Publisher: Wspc, 2014

Synopsis

“This is a very nice text on some important topics on commutative ring theory.” Mathematical Association of America 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.

About this title

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

About this edition

• Publisher: Wspc
• Publication date: 2014
• ISBN 10: 9814603651
• ISBN 13: 9789814603652
• Binding: Hardcover
• Number of pages: 224
• Editor: Nielsen Holger Andreas