Algebra · Chapter VIII

Semisimple Modules and Rings

Semisimple Modules and Rings 0 statements
§ 1. Artinian Modules and Noetherian Modules 36 statements · 28 exercises
§ 2. The Structure of Modules of Finite Length 37 statements · 20 exercises
§ 3. Simple Modules 23 statements · 10 exercises
§ 4. Semisimple Modules 43 statements · 8 exercises
§ 5. Commutation 37 statements · 19 exercises
§ 6. Morita Equivalence of Modules and Algebras 40 statements · 8 exercises
§ 7. Simple Rings 24 statements · 16 exercises
§ 8. Semisimple Rings 30 statements · 6 exercises
§ 9. Radical 49 statements · 31 exercises
§ 10. Modules over an Artinian Ring 12 statements · 11 exercises
§ 11. Grothendieck Groups 38 statements · 14 exercises
§ 12. Tensor Products of Semisimple Modules 26 statements · 17 exercises
§ 13. Absolutely Semisimple Algebras 33 statements · 12 exercises
§ 14. Central Simple Algebras 36 statements · 19 exercises
§ 15. Brauer Groups 12 statements · 2 exercises
§ 16. Other Descriptions of the Brauer Group 63 statements · 17 exercises
§ 17. Reduced Norms and Traces 31 statements · 7 exercises
§ 18. Simple Algebras over a Finite Field 10 statements · 7 exercises
§ 19. Quaternion Algebras 16 statements · 8 exercises
§ 20. Linear Representations of Algebras 31 statements · 6 exercises
§ 21. Linear Representations of Finite Groups 36 statements · 30 exercises
App. 1. Algebras without Unit Element 20 statements · 15 exercises
App. 2. Determinants over a Noncommutative Field 18 statements · 4 exercises
App. 3. Hilbert’s Nullstellensatz 3 statements
App. 4. Trace of an Endomorphism of Finite Rank 5 statements · 2 exercises
Historical Note 0 statements