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Title

Modules commuting (via Hom) with some limits

Authors 1, 1

Affiliations

  1. KA MFF UK, Sokolovská 83, 186 00 Praha 8 - Karlín, Czech Republic

Abstract

For every module M we have a natural monomorphism  Φ:∐i∈IHomR(Ai,M)→HomR(∏i∈IAi,M) and we focus attention on the case when Φ is also an epimorphism. The corresponding modules M depend on thickness of the cardinal number card(I). Some other limits are also considered.

Bibliography

  1. D. Allouch, Modules maigres, thèse, Montpellier, 1969/70.
  2. L. Bican, J. Jirásko, T. Kepka and B. Torrecillas, Modules and their extensions I. (Purities), Publ. Dept. Math. M93001 (1993), Faculty of Civil Engin., Czech Techn. Univ., Prague.
  3. R. Dimitrić, Slender modules over domains, Comm. Algebra 11 (1983), 1685-1700.
  4. R. Dimitrić, Slenderness in abelian categories, in: Abelian Group Theory, Lecture Notes in Math. 1006, Springer, 1983, 375-383.
  5. K. Eda, A Boolean power and a direct product of abelian groups, Tsukuba J. Math. 6 (1982), 187-193.
  6. K. Eda, On a Boolean power of a torsion free Abelian group, J. Algebra 82 (1983), 84-93.
  7. K. Eda, Slender modules, endo-slender abelian groups and large cardinals, Fund. Math. 135 (1990), 5-24.
  8. A. Ehrenfeucht and J. Łoś, Sur les produits cartésiens des groupes cycliques infinies, Bull. Acad. Polon. Sci. Sér. Astronom. Phys. Sci. Math. 2 (1954), 261-263.
  9. P. Eklof and A. Mekkler, Almost Free Modules, North-Holland, 1990.
  10. R. El Bashir and T. Kepka, On when small semiprime rings are slender, Comm. Algebra 24 (1996), 1575-1580.
  11. R. El Bashir and T. Kepka, Notes on slender prime rings, Comment. Math. Univ. Carolin. 37 (1996), 419-422.
  12. R. El Bashir, T. Kepka and P. Němec, Modules commuting (via Hom) with some colimits, preprint.
  13. L. Fuchs, Abelian Groups, Pergamon Press, 1960.
  14. L. Fuchs, Infinite Abelian Groups, Vol. I, Academic Press, 1970.
  15. L. Fuchs, Infinite Abelian Groups, Vol. II, Academic Press, 1973.
  16. L. Fuchs and L. Salce, Modules over Valuation Domains, M. Dekker, 1985.
  17. G. Heinlein, Vollreflexive Ringe und schlanke Moduln, Dissertation, Erlangen, 1971.
  18. L. Henkin, A problem on inverse mapping systems, Proc. Amer. Math. Soc. 1 (1950), 224-225.
  19. A. Kanamori, The Higher Infinite, Springer, 1994.
  20. S. Koppelberg, Handbook of Boolean Algebras, Vol. I, North-Holland, 1989.
  21. E. Lady, Slender rings and modules, Pacific J. Math. 49 (1973), 397-406.
  22. A. Mader, Groups and modules that are slender as modules over their endomorphism rings, in: Abelian Groups and Modules, CISM Courses and Lectures 287, Springer, 1984, 315-327.
  23. G. de Marco and A. Orsatti, Complete linear topologies on abelian groups, Sympos. Math. 13 (1974), 153-161.
  24. R. Nunke, Slender groups, Acta Sci. Math. (Szeged) 23 (1962), 67-73.
  25. A. Pultr and V. Trnková, Combinatorial, Algebraic and Topological Representations of Groups, Semigroups and Categories, North-Holland, 1980.
  26. L. Salce, Moduli slender su anelli di Dedekind, Ann. Univ. Ferrara Sez. VII Sci. Math. 20 (1975), 59-63.
  27. E. Sąsiada, Proof that every countable and reduced torsion-free abelian group is slender, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 7 (1959), 143-144.
  28. J. Trlifaj, Similarities and differences between abelian groups and modules over non-perfect rings, in: Contemp. Math. 171 Amer. Math. Soc., 1994, 397-406.
  29. R. Wisbauer, Grundlagen der Modul und Ringtheorie, R. Fisher, 1988.
Fundamenta Mathematicae
1998/155/3
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Pages:
271-292
Main language of publication
English
Received
1996-11-14
Accepted
1997-09-23
Published
1998
Exact and natural sciences