Hostname: page-component-8448b6f56d-c4f8m Total loading time: 0 Render date: 2024-04-20T02:45:21.178Z Has data issue: false hasContentIssue false
  • English
  • Français

Constructing pure injective hulls

Published online by Cambridge University Press:  12 March 2014

Wilfrid Hodges
Wilfrid Hodges*
Affiliation:
Bedford College, London, England
Get access Rights & Permissions [Opens in a new window]

Extract

Let A be an abelian group and B a pure injective pure extension of A. Then there is a homomorphic image C of B over A which is a pure injective hull of A; C can be constructed by using Zorn's lemma to find a suitable congruence on B. In a paper [4] which greatly generalises this and related facts about pure injectives, Walter Taylor asks (Problem 1.5) whether one can find a “construction” of C which is more concrete than the one mentioned above; he asks also whether the points of C can be explicitly described. In this note I return the answer No.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 45 , Issue 3 , September 1980 , pp. 544 - 548
Copyright
Copyright © Association for Symbolic Logic 1980

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Fuchs, László, Infinite abelian groups. I, Academic Press, New York, 1970.Google Scholar
[2]Hodges, Wilfrid, On the effectivity of some field constructions, Proceedings of the London Mathematical Society, vol. 32 (1976), pp. 133–162.CrossRefGoogle Scholar
[3]Hodges, Wilfrid, A normal form for algebraic constructions. II, Six days of model theory. (Henrard, Paul, Editor), Castella, Albeuve, 1977 (reprinted from Logiqueet Analyse, vol. 71/72 (1975), pp. 429–487).Google Scholar
[4]Taylor, Walter, Some constructions of compact algebras, Annals of Mathematical Logic, vol. 3 (1971), pp. 395–437.CrossRefGoogle Scholar