Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-26T20:21:44.559Z Has data issue: false hasContentIssue false
  • English
  • Français

A Problem on Relative Projectivity for Abelian Groups

Published online by Cambridge University Press:  20 November 2018

S. Feigelstock  and
R. Raphael
S. Feigelstock
Affiliation:
Bar-Ilan UniversityRamat-Gan, Israel
R. Raphael
Affiliation:
Bar-Ilan UniversityRamat-Gan, Israel
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The article studies the class of abelian groups G such that in every direct sum decomposition G = A ⊕ B, A is 5-projective. Such groups are called pds groups and they properly include the quasi-projective groups.

The pds torsion groups are fully determined.

The torsion-free case depends on a lemma that establishes freedom in the non-indecomposable case for several classes of groups. There is evidence suggesting freedom in the general reduced torsion-free case but this is not established and prompts a logical discussion. It is shown, for example, that pds torsion-free groups must be Whitehead if they are not indecomposable, but that there exists Whitehead groups that are not pds if there exist non-free Whitehead groups.

The mixed case is characterized and examples are given.

Keywords

abelian groupprojectivitymodule13C1020K40
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 29 , Issue 1 , 01 March 1986 , pp. 114 - 122
Copyright
Copyright © Canadian Mathematical Society 1986

References

1. Azumaya, G., Mbuntun, F., and Varadarajan, K., On M-projective and M-injective modules, Pac. J. Math. 59 (1975), pp. 9–16.Google Scholar
2. Burgess, W. and Raphael, R., Sur les modules à facteurs directs absolus, (submitted).Google Scholar
3. Fuchs, L., Abelian Groups, Pergamon Press, N.Y., 1960.Google Scholar
4. Fuchs, L., Infinite Abelian Groups, Vol. I, Academic Press, New York-London, 1971.Google Scholar
5. Fuchs, L., Infinite Abelian Groups, Vol. II, Academic Press, New York-London, 1973.Google Scholar
6. Fuchs, L. and Rangaswamy, K., Quasi-projective abelian groups, Bull Soc. Math., France 98 (1970), pp. 5–8.Google Scholar