Basic subgroups and freeness, a counterexample

Kapitel in diesem Buch

1. Frontmatter I
2. Contents VII
3. Anthony Leonard Southern Corner 1934–2006 1
4. Groups of units of orders in Q-algebras 9
5. Basic subgroups and freeness, a counterexample 63
6. An extension of Butler’s theorem on endomorphism rings 75
7. Locally free abelian groups of finite rank 83
8. Decompositions of global crq-groups 99
9. Endomorphisms and automorphisms of squares of abelian groups 121
10. Classification of a class of finite rank Butler groups 135
11. Quotient divisible and almost completely decomposable groups 147
12. Pure subgroups of completely decomposable groups – an algorithmic approach 169
13. Strong subgroup chains and the Baer–Specker group 187
14. On direct decompositions of Butler B(2)-groups 199
15. Diagonal equivalence of matrices 219
16. Root bases of polynomials over integral domains 235
17. A solution to a problem on lattice isomorphic Abelian groups 249
18. A note on Axiom 3 and its dual for abelian groups 257
19. Units of modular p-mixed abelian group algebras 267
20. Pure covers in abelian p-groups 277
21. Partially decomposable primary Abelian groups and the generalized core class property 289
22. The additive group of a finite local ring in which each ideal can be n-generated 301
23. A Jacobson radical isomorphism theorem for torsion-free modules 309
24. Anti-isomorphisms and the failure of duality 315
25. Automorphism groups of models of first order theories 325
26. The classification problem for finite rank Butler groups 329
27. L-groups 339
28. Co-local subgroups of nilpotent groups of class 2 351
29. Divisible envelopes and cotorsion pairs over integral domains 359
30. The first Brauer–Thrall conjecture 369
31. A version of the Baer splitting problem for noetherian rings 375
32. Characterizations and constructions of h-local domains 385
33. Variations on Whitehead’s problem and the structure of Ext 407
34. The lattice of torsionfree precover classes 415
35. Non-singular rings of injective dimension 1 421
36. On classes defining a homological dimension 431
37. Truncated path algebras are homologically transparent 445
38. Representations of the category of serial modules of finite Goldie dimension 463
39. Commutativity modulo small endomorphisms and endomorphisms of zero algebraic entropy 487