Modules over Endomorphism Rings
Modules over Endomorphism Rings
$160.00
USDThis 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.
- Contains over 200 exercises as well as problems for further research
- Serves as an introduction for graduate students wishing to study modules over endomorphism rings and related problems
- Presents results and perspectives that are not available elsewhere
Reviews & endorsements
"This monograph is an up-to-date account of the intermingling of the theory of rtffr groups, ring theory, module theory, and number theory. Any researcher working in any of these areas should have a copy of this book."
Manfred Dugas, Mathematical Reviews
"Theodore Faticoni enriches the mathematical literature with a comprehensive and up-to-date account of the study of a large class of abelian groups, presenting all the relevant results in a very well organized fashion, most of which have been obtained by the author since the 1970s."
Nadia Mazza, Bulletin of the London Mathematical Society
Product details
November 2009Hardback
9780521199605
392 pages
240 × 160 × 25 mm
0.73kg
210 exercises
Available
Table of Contents
- 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.
