Skip to main content

On k-Products Modulo μ-Products

  • Chapter

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

Abstract

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}.

Keywords

  • 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.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S. Balcercyk, On groups of functions defined on Boolean algebras, Fund. Math. 50 (1962) 347–367.

    Google Scholar 

  2. H.D. Donder, in preparation.

    Google Scholar 

  3. M. Dugas and G. Herden; Arbitrary torsion classes and almost free abelian groups, to appear in Israel J.

    Google Scholar 

  4. L. Fuchs, Infinite Abelian groups II, Academic Press, New York 1974.

    Google Scholar 

  5. R. Göbel and S. Shelah, Semi-rigid classes of cotorsionfree abelian groups, submitted to J. Algebra.

    Google Scholar 

  6. R. Göbel and B. Wald, Wachstumstypen und schlanke Gruppen, Symp. Math. 23 (1979) 201–239.

    Google Scholar 

  7. R. Göbel and B. Wald, Lösung eines Problems von L. Fuchs, J. Algebra, 71 (1981) 219–231.

    CrossRef  Google Scholar 

  8. 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. T. Jech, Set Theory, Academic Press, New York, London (1978).

    Google Scholar 

  10. J. Lo’s, Linear equations and pure subgroups, Bull. Acad. Polon. Sci., 7 (1959) 13–18.

    Google Scholar 

  11. E. Sasiada, Proof that every countable and reduced torsionfree abelian group is slender, Bull. Acad. Polon. Sci., 7 (1959) 143–144.

    Google Scholar 

  12. B. Wald, Martinaxiom und die Beschreibung gewisser Homomorphismen in der Theorie der g1 -freien abelschen Gruppen, to appear in Manuscr. Math.

    Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1983 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Wald, B. (1983). On k-Products Modulo μ-Products. In: Göbel, R., Lady, L., Mader, A. (eds) Abelian Group Theory. Lecture Notes in Mathematics, vol 1006. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21560-9_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-21560-9_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12335-4

  • Online ISBN: 978-3-662-21560-9

  • eBook Packages: Springer Book Archive