On k-Products Modulo μ-Products

  • Burkhard Wald
Part of the Lecture Notes in Mathematics book series (LNM, volume 1006)


1. For a set I and a family (Ai)i∈i of abelian groups consider the cartesian product \( \mathop \pi \limits_{i \in I} {A_i}, \) which is in a natural way an abelian group iEI again. The support of an element x of \( \mathop \pi \limits_{i \in I} {A_i}, \)is defined by supp(x) {=i ∈ I: x(i) ≠ 0}.


Abelian Group Compact Group Direct Summand Measurable Cardinal Pure Subgroup 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [B]
    S. Balcercyk, On groups of functions defined on Boolean algebras, Fund. Math. 50 (1962) 347–367.Google Scholar
  2. [D]
    H.D. Donder, in preparation.Google Scholar
  3. [DH]
    M. Dugas and G. Herden; Arbitrary torsion classes and almost free abelian groups, to appear in Israel J.Google Scholar
  4. [F]
    L. Fuchs, Infinite Abelian groups II, Academic Press, New York 1974.Google Scholar
  5. [GS]
    R. Göbel and S. Shelah, Semi-rigid classes of cotorsionfree abelian groups, submitted to J. Algebra.Google Scholar
  6. [GW1]
    R. Göbel and B. Wald, Wachstumstypen und schlanke Gruppen, Symp. Math. 23 (1979) 201–239.Google Scholar
  7. [GW2]
    R. Göbel and B. Wald, Lösung eines Problems von L. Fuchs, J. Algebra, 71 (1981) 219–231.CrossRefGoogle Scholar
  8. [GWW]
    R. Göbel, B. Wald and P. Westphal, Groups of integer-valuated functions, in Abelian Group Theory, Proceedings, Oberwolfach 1981, Springer Lecture Notes, 874 (1981) 161–178.Google Scholar
  9. [J]
    T. Jech, Set Theory, Academic Press, New York, London (1978).Google Scholar
  10. [L]
    J. Lo’s, Linear equations and pure subgroups, Bull. Acad. Polon. Sci., 7 (1959) 13–18.Google Scholar
  11. [S]
    E. Sasiada, Proof that every countable and reduced torsionfree abelian group is slender, Bull. Acad. Polon. Sci., 7 (1959) 143–144.Google Scholar
  12. [W]
    B. Wald, Martinaxiom und die Beschreibung gewisser Homomorphismen in der Theorie der g1 -freien abelschen Gruppen, to appear in Manuscr. Math.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • Burkhard Wald

There are no affiliations available

Personalised recommendations