Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-26T13:21:17.239Z Has data issue: false hasContentIssue false
  • English
  • Français

A New Construction of the Injective Hull

Published online by Cambridge University Press:  20 November 2018

Isidore Fleischer
Isidore Fleischer*
Affiliation:
Queens University
Rights & Permissions [Opens in a new window]

Extract

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 definition of injectivity, and the proof that every module has an injective extension which is a subextension of every other injective extension, are due to R. Baer [B]. An independent proof using the notion of essential extension was given by Eckmann-Schopf [ES]. Both proofs require the p reliminary construction of some injective overmodule. In [F] I showed how the latter proof could be freed from this requirement by exhibiting a set F in which every essential extension could be embedded. Subsequently J. M. Maranda pointed out that F has minimal cardinality. It follows that F is equipotent with the injective hull. Below Icon struct the injective hull by equipping Fit self with a module strucure.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 11 , Issue 1 , April 1968 , pp. 19 - 21
Copyright
Copyright © Canadian Mathematical Society 1968

References

B Baer, R., Abelian groups that are direct summands of every containing abelian group, Bull. Am. Math. Soc. 46 (1940) 800-806.10.1090/S0002-9904-1940-07306-9Google Scholar
ES Eckmann, B. und Schopf, A., Über injektive Moduln, Arch. Math. 4 (1953) 75-78.10.1007/BF01899665Google Scholar
F Fleischer, I., Sur le problème d'application universelle de M. Bourbaki, C.R. Acad. Sci. Paris 254 (1962) 3161-3163.Google Scholar