Modules over Endomorphism Rings

Theodore G. Faticoni is Associate Professor in the Mathematics Department at Fordham University, New York.

• 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.

'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 organised fashion … the book is a succession of very sharp results, which are the fruits of methodical and thorough investigations started about 40 years ago by the author. Page after page, Faticoni engages the reader in a friendly mathematical discussion. As incentive, he provides some historical motivations for the questions he considers, for example, the classification of algebraic number fields, which goes back to Gauss and Kummer, while numerous examples, exercises and problems for future research at the end of each chapter will certainly provide the reader with some stimulating challenges.' Bulletin of the London Mathematical Society