Endomorphism Rings of Abelian Groups by P.A. Krylov (PDF)

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Preface. Symbols. I: General Results on Endomorphism Rings. 1. Rings, Modules and Categories. 2. Abelian Groups. 3. Examples and Some Properties of Endomorphism Rings. 4. Torsion-Free Rings of Finite Rank. 5. Quasi-Endomorphism Rings of Torsion-Free Groups. 6. E-Modules and E-Rings. 7. Torsion-Free Groups Coinciding with Their Pseudo-Socles. 8. Irreducible Torsion-Free Groups. II: Groups as Modules over Their Endomorphism Rings. 9. Endo-Artinian and Endo-Noetherian Groups. 10. Endo-Flat Primary Groups. 11. Endo-Finite Torsion-Free Groups of Finite Rank. 12. Endo-Projective and Endo-Generator Torsion-Free Groups of Finite Rank. 13. Endo-Flat Torsion-Free Groups of Finite Rank. III: Ring Properties of Endomorphism Rings. 14. The Finite Topology. 15. Endomorphism Rings with the Minimum Condition. 16. Hom(A, B) as a Noethian Module over End(£Ii£). 18. Regular Endomorphism Rings. 19. Commutative and Local Endomorphism Rings. IV: The Jacobson Radical of the Endomorphism Ring. 20. The Case of p-groups. 21. The Radical of the Endomorphism Ring of a Torsion-Free Group of Finite Rank. 22. The Radical of the Endomorphism Ring of Algebraically Compact and Completely Decomposable Torsion-Free Groups. 23. The Nilpotence of the Radicals N (End(G)) and J (End(G)). V: Isomorphism and Realization Theorems. 24. The Baer Kaplansky Theorem. 25. Continuous and Discrete Isomorphisms of Endomorphism Rings. 26. Endomorphism Rings of Groups with Large Divisible Subgroups. 27. Endomorphism Rings of Mixed Groups of Torsion-Free Rank 1. 28. The Corner Theorem on Split Realization. 29. Realizations for Endomorphism Rings of Torsion-Free Groups. 30. The Realization Problem for Endomorphism Rings of Mixed Groups. VI: Hereditary Endomorphism Rings. 31.Self-Small Groups. 32. Categories of Groups andModules over Endomorphism Rings. 33. Faithful Groups. 34. Faithful Endo-Flat Groups. 35. Groups with Right Hereditary Endomorphism Rings. 36. Groups of Generalized Rank 1. 37. Torsion-Free Groups with Hereditary Endomorphism Rings. 38. Maximal Orders as Endomorphism Rings. 39. p-Semisimple Groups. VII: Fully Transitive Groups. 40. Homogeneous Fully Transitive Groups. 41. Groups whose Quasi-Endomorphism Rings are Division Rings. 42. Fully Transitive Groups Coinciding with Their Pseudo-Socles. 43. Fully Transitive Groups with Restrictions on Element Types. 44. Torsion-Free Groups of p-Ranks = 1. References. Index.

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