Small almost free modules with prescribed topological endomorphism rings
A. L. S. Corner; Rüdiger Göbel
Rendiconti del Seminario Matematico della Università di Padova (2003)
- Volume: 109, page 217-234
- ISSN: 0041-8994
Access Full Article
topHow to cite
topReferences
top- [1] R. BAER, Abelian groups without elements of finite order, Duke Math. J., 3 (1937), pp. 68-122. Zbl0016.20303MR1545974JFM63.0074.02
- [2] A. BIRTZ, Sur des décompositions directes paradoxales de groupes abéliens sans torsion, Abelian Group Theory, Proceedings, Honolulu 1982/83, Lecture Notes in Mathematics 1006 (Springer, Berlin, 1983), pp. 358-361. Zbl0517.20029MR722630
- [3] A. L. S. CORNER, Every countable reduced torsion-free ring is an endomorphisms ring, Proc. London Math. Soc., 13 (1963), pp. 687-710. Zbl0116.02403MR153743
- [4] A. L. S. CORNER, Endomorphisms rings of torsion-free abelian groups, Proceedings of the International Conference on the Theory of Groups, Canberra 1965 (Gordon and Breach, New York, 1967), pp. 59-69. Zbl0178.02303
- [5] A. L. S. CORNER, Additive categories and a theorem of W. G. Leavitt, Bull. Amer. Math. Soc., 75 (1969), pp. 78-82. Zbl0188.08502MR238903
- [6] A. L. S. CORNER, On the existence of very decomposable abelian groups, Abelian Group Theory, Proceedings, Honolulu 1982/83, Lecture Notes in Mathematics 1006 (Springer, Berlin, 1983), pp. 354-357. MR722629
- [7] A. L. S. CORNER - R. GÖBEL, Prescribing endomorphism algebras, a unified treatment, Proc. London Math. Soc., 50 (1985), pp. 447-479. Zbl0562.20030MR779399
- [8] M. DUGAS - R. GÖBEL, Every cotorsion-free ring is an endomorphism ring, Proc. London Math. Soc. (3), 45 (1982), pp. 319-336. Zbl0506.16022MR670040
- [9] M. DUGAS - R. GÖBEL, Every cotorsion-free algebra is an endomorphism algebra, Math. Zeitschr., 181 (1982), pp. 451-470. Zbl0501.16031MR682667
- [10] P. C. EKLOF, Set theoretic methods in homological algebra and abelian groups, Les Presses de l’Université de Montréal, Montreal 1980. Zbl0488.03029MR565449
- [11] K. EDA, Cardinal restrictions for preradicals, Abelian Group Theory, Contemporary Math. 87, Providence, 1989, pp. 277-283. Zbl0687.20049MR995283
- [12] P. EKLOF - A. MEKLER, Almost Free Modules, Set-theoretic Methods, NorthHolland, 1990. Zbl0718.20027MR1055083
- [13] L. FUCHS, Abelian Groups, Vol. I and II, Academic Press, 1970 and 1973.
- [14] R. GÖBEL, Some combinatorial principles for solving algebraic problems, Infinite length modules, Trends in Mathematics, Birkhäuser Verlag, Basel, 2000, pp. 107-127. Zbl0985.20047MR1789212
- [15] R. GÖBEL - S. SHELAH, Indecomposable almost free modules—the local case, Canadian J. Math., 50 (4) (1998), pp. 719-738. Zbl0959.20049MR1638607
- [16] R. GÖBEL - S. SHELAH, Endomorphism rings of modules whose cardinality is cofinal to v, Abelian groups, module theory, and topology, Marcel Dekker, New York, 1998, pp. 235-248. Zbl0940.16016MR1651170
- [17] P GRIFFITH, ]n-free abelian groups, Quart. J. Math. (2), 23 (72), pp. 417-425. Zbl0274.20068MR325804
- [18] T. JECH, Set theory, Academic Press, New York, 1978. Zbl0419.03028MR506523
- [19] S. SHELAH, On uncountable abelian groups, Israel J. Math., 32 (1979), pp. 311-330. Zbl0412.20047MR571086
- [20] S. SHELAH, On endo-rigid strongly ]1-free abelian groups in ]1 , Israel J. Math., 40 (1981), pp. 291-295. Zbl0501.03015MR654584
- [21] S. SHELAH, A combinatorial theorem and endomorphism rings of abelian groups II, Abelian Groups and Modules (R. Göbel, C. Metelli, A. Orsatti and L. Salce, eds.), CISM Courses and Lectures 287, Springer-Verlag, 1984, pp. 37-86. Zbl0581.20052MR789808