Description
CAMBRIDGE Modules over Endomorphism Rings 2009 Edition by Theodore G. Faticoni
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. 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.