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Constructing pure injective hulls

Published online by Cambridge University Press:  12 March 2014

Wilfrid Hodges
Wilfrid Hodges*
Affiliation:
Bedford College, London, England
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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

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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