Preface Part I. The Structure of Group Algebras: 1. Idempotents in rings. Liftings 2. Projective and injective modules 3. The radical and artinian rings 4. Cartan invariants and blocks 5. Finite dimensional algebras 6. Duality 7. Symmetry 8. Loewy series and socle series 9. The p. i. m.'s 10. Ext 11. Orders 12. Modular systems and blocks 13. Centers 14. R-forms and liftable modules 15. Decomposition numbers and Brauer characters 16. Basic algebras and small blocks 17. Pure submodules 18. Examples Part II. Indecomposable Modules and Relative Projectivity: 1. The trace map and the Nakayama relations 2. Relative projectivity 3. Vertices and sources 4. Green Correspondence 5. Relative projective homomorphisms 6. Tensor products 7. The Green ring 8. Endomorphism rings 9. Almost split sequences 10. Inner products on the Green ring 11. Induction from normal subgroups 12. Permutation models 13. Examples Part III. Block Theory: 1. Blocks, defect groups and the Brauer map 2. Brauer's First Main Theorem 3. Blocks of groups with a normal subgroup 4. The Extended First main Theorem 5. Defect groups and vertices 6. Generalized decomposition numbers 7. Subpairs 8. Characters in blocks 9. Vertices of simple modules 10. Defect groups Appendices References Index.
Preface Part I. The Structure of Group Algebras: 1. Idempotents in rings. Liftings 2. Projective and injective modules 3. The radical and artinian rings 4. Cartan invariants and blocks 5. Finite dimensional algebras 6. Duality 7. Symmetry 8. Loewy series and socle series 9. The p. i. m.'s 10. Ext 11. Orders 12. Modular systems and blocks 13. Centers 14. R-forms and liftable modules 15. Decomposition numbers and Brauer characters 16. Basic algebras and small blocks 17. Pure submodules 18. Examples Part II. Indecomposable Modules and Relative Projectivity: 1. The trace map and the Nakayama relations 2. Relative projectivity 3. Vertices and sources 4. Green Correspondence 5. Relative projective homomorphisms 6. Tensor products 7. The Green ring 8. Endomorphism rings 9. Almost split sequences 10. Inner products on the Green ring 11. Induction from normal subgroups 12. Permutation models 13. Examples Part III. Block Theory: 1. Blocks, defect groups and the Brauer map 2. Brauer's First Main Theorem 3. Blocks of groups with a normal subgroup 4. The Extended First main Theorem 5. Defect groups and vertices 6. Generalized decomposition numbers 7. Subpairs 8. Characters in blocks 9. Vertices of simple modules 10. Defect groups Appendices References Index.
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