Modules over Endomorphism Rings: 130 (Encyclopedia of Mathematics and its Applications, Series Number 130)
Cambridge University Press
Edition: Illustrated, 10/22/2009
EAN 9780521199605, ISBN10: 0521199603
Hardcover, 392 pages, 24.1 x 16 x 2.5 cm
Language: English
This is an extensive synthesis of recent work in the study of endomorphism rings and their modules, bringing together direct sum decompositions of modules, the class number of an algebraic number field, point set topological spaces, and classical noncommutative localization. The main idea behind the book is to study modules G over a ring R via their endomorphism ring EndR(G). The author discusses a wealth of results that classify G and EndR(G) via numerous properties, and in particular results from point set topology are used to provide a complete characterization of the direct sum decomposition properties of G. For graduate students this is a useful introduction, while the more experienced mathematician will discover that the book contains results that are not otherwise available. Each chapter contains a list of exercises and problems for future research, which provide a springboard for students entering modern professional mathematics.
Preface
1. Preliminary results
2. Class number of an Abelian group
3. Mayer-Vietoris sequences
4. Lifting units
5. The conductor
6. Conductors and groups
7. Invertible fractional ideals
8. L-Groups
9. Modules and homotopy classes
10
Tensor functor equivalences
11. Characterizing endomorphisms
12. Projective modules
13. Finitely generated modules
14. Rtffr E-projective groups
15. Injective endomorphism modules
16. A diagram of categories
17. Diagrams of Abelian groups
18. Marginal isomorphisms
References
Index.