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

How to cite

top

Corner, A. L. S., and Göbel, Rüdiger. "Small almost free modules with prescribed topological endomorphism rings." Rendiconti del Seminario Matematico della Università di Padova 109 (2003): 217-234. <http://eudml.org/doc/108600>.

@article{Corner2003,
author = {Corner, A. L. S., Göbel, Rüdiger},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {realization of topological rings as endomorphism rings; -free Abelian groups; direct sums; pathological Abelian groups; endomorphisms; modules over commutative rings},
language = {eng},
pages = {217-234},
publisher = {Seminario Matematico of the University of Padua},
title = {Small almost free modules with prescribed topological endomorphism rings},
url = {http://eudml.org/doc/108600},
volume = {109},
year = {2003},
}

TY - JOUR
AU - Corner, A. L. S.
AU - Göbel, Rüdiger
TI - Small almost free modules with prescribed topological endomorphism rings
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 2003
PB - Seminario Matematico of the University of Padua
VL - 109
SP - 217
EP - 234
LA - eng
KW - realization of topological rings as endomorphism rings; -free Abelian groups; direct sums; pathological Abelian groups; endomorphisms; modules over commutative rings
UR - http://eudml.org/doc/108600
ER -

References

top
  1. [1] R. BAER, Abelian groups without elements of finite order, Duke Math. J., 3 (1937), pp. 68-122. Zbl0016.20303MR1545974JFM63.0074.02
  2. [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. [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. [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. [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. [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. [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. [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. [9] M. DUGAS - R. GÖBEL, Every cotorsion-free algebra is an endomorphism algebra, Math. Zeitschr., 181 (1982), pp. 451-470. Zbl0501.16031MR682667
  10. [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. [11] K. EDA, Cardinal restrictions for preradicals, Abelian Group Theory, Contemporary Math. 87, Providence, 1989, pp. 277-283. Zbl0687.20049MR995283
  12. [12] P. EKLOF - A. MEKLER, Almost Free Modules, Set-theoretic Methods, NorthHolland, 1990. Zbl0718.20027MR1055083
  13. [13] L. FUCHS, Abelian Groups, Vol. I and II, Academic Press, 1970 and 1973. 
  14. [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. [15] R. GÖBEL - S. SHELAH, Indecomposable almost free modules—the local case, Canadian J. Math., 50 (4) (1998), pp. 719-738. Zbl0959.20049MR1638607
  16. [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. [17] P GRIFFITH, ]n-free abelian groups, Quart. J. Math. (2), 23 (72), pp. 417-425. Zbl0274.20068MR325804
  18. [18] T. JECH, Set theory, Academic Press, New York, 1978. Zbl0419.03028MR506523
  19. [19] S. SHELAH, On uncountable abelian groups, Israel J. Math., 32 (1979), pp. 311-330. Zbl0412.20047MR571086
  20. [20] S. SHELAH, On endo-rigid strongly ]1-free abelian groups in ]1 , Israel J. Math., 40 (1981), pp. 291-295. Zbl0501.03015MR654584
  21. [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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.