Cotorsion theories and splitters

Transactions of the American Mathematical Society

Volumn 352, Issue 11, 2000, Pages 5357-5379

  Göbel, Rüdiger ^a   Shelah, Saharon ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

Completions; Cotorsion theories; Enough pro jectives; Realizing rings as endomorphism rings of self splitting modules; Self splitting modules

Indexed keywords

EID: 23044522416     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-00-02475-2     Document Type: Article

References (27)

1. T. Bccker, L. Fuchs, S. Shelah, \Vhitehead modules over domains, Forum Mathematicum (1989), 53-68. MR 90a:13017
2. A.L.S. Corner, R. Göbel, Prescribing endomorphism algebras - A unified treatment, Proceed London Math. Soc. (3) 50 (1985), 447-479. MR 86h:16031
3. S. E. Dickson, A torsion theory for abelian categories, Trans. Amer. Math. Soc. 121 (1966) 223-235. MR 35:162
4. P. Eklof, A. Mekler, Almost free modules, Set-theoretic methods, North-Holland, Amsterda 1990. MR 92o:20001
5. B. Franzen, R. Göbel, Presribing endomorphism algeras. The cotorsion-free case. Rend. Sem Mat. Padova 80 (1989), 215 - 241. MR 90h:16050
6. L. Fuchs, Infinite abelian groups - Volume 1,2, Academic Press, New York (1970, 1972) M 41:333; MR 50:2362
7. P. A. Griffith, A solution of the splitting mixed problem of Baer, Trans. American Math. Soc 139 (1969), 261-269. MR 39:317
8. R. Göbel, Abelian groups with only small cotorsion images, J. Austral. Math. Soc. (Ser. A 50 (1991), 243-247. MR 91m:20075
9. R. Göbel, New aspects for two classical theorems on torsion splitting, Comm. Algebra 15 (1987), 2473-2495. MR 89h:13019
10. R. Göbel, R. Prelle, Solution of two problems on cotorsion abelian groups, Archiv der Math 31 (1978), 423131. MR 80f:20063
11. R. Göbel, S. Shelah, Almost free splitters, Colloq. Math. 81 (1999), 193-221.
12. R. Göbel, J. Trlifaj, Cotilting and a hierarchy of almost cotorsion groups, to appear in Proc Amer. Math. Soc.
13. J. Hausen, Automorphismen gesättigte Klassen abzählbarer abelschen Gruppen, Studies o Abelian Groups, Springer, Berlin (1968), 147-181. MR 39:5691
14. T. Jech, Set Theory, Academic Press, New York (1978). MR 80a:03062
15. O. Kerner, Elementary stones, Comm. Algebra, 22 (1994) 1797 - 1806. MR 95d:16017
16. M. Prest, Model theory and modules, London Math. Soc. L.N. 130 Cambridge Universit Press 1988. MR 89h:034061
17. C. M. Ringel, The braid group action on the set of exceptional sequences of a hereditary artin algebra, pp. 339 -352 in Abelian group theory and related topics, Contemporary Math. 171, American Math. Soc., Providence, R.I. 1994. MR 95m:16006
18. C. M. Ringel, Bricks in hereditary length categories, Resultate der Mathematik 6 (1983) 64-70. MR 85a:16035
19. P. Rothmaler, Purity in model theory, pp. 445 - 4G9 in Advances in Algebra and Mode Theory, Series Algebra, Logic and Applications, Vol. 9, Gordon and Breach, Amsterda 1997. CMP 99:12
20. A. N. Rudakov, Helices and vector bundles, London Math. Soc. Lecture Note Ser. LNM 148 MR 91e:14002
21. L. Sake, Cotorsion theories for abelian groups, Symposia Math. 23 (1979), 11-32. M 81j:20078
22. P. Schultz, Self-splitting'groups, Preprint series of the University of Western Australia a Perth (1980).
23. S. Shelah, A combinatorial theorem and endomorphism rings of abelian groups II, pp. 37 86, in Abelian groups and modules, CISM Courses and Lectures, 287, Springer, Wien 1984 MR 86i:20075
24. L. Unger, Schur modules over wild, finite dimensional path algebras with three simple modules, Journal Pure Appl. Algebra 64 (1990) 205 - 222. MR 91i: 16034
25. T. Wakamatsu, On modules with trivial self-extensions, Journal of Algebra 114 (1988), 106 114. MR 89b:16020
26. R. Warfield, Purity and algebraic compactness for modules, Pacific J. Math. 28 (1969) 699 - 719. MR 39:4212
27. M. Ziegler, Model theory of modules, Ann. Pure Appl. Logic 26 (1984) 149 - 213. M 86c:03034