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On Injective Sheaves

Published online by Cambridge University Press:  20 November 2018

H. Kleisli  and
Y.C. Wu
H. Kleisli
Affiliation:
University of Ottawa
Y.C. Wu
Affiliation:
University of Ottawa
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A divisible abelian group D can be characterized by the following property: Every homomorphism from an abelian group A to D can be extended to every abelian group B containing A. This together with the result that every abelian group can be embedded in a divisible group is a crucial point in many investigations on abelian groups. It was Baer, [1], who extended this result to modules over an arbitrary ring, replacing divisible groups by injective modules, that is, modules with the property mentioned above. Another proof was found later by Eckmann and Schopf, [3]. This proof assumes the proposition to hold for abelian groups and transfers it in a very simple and elegant manner to modules. In the sequel, we shall refer to this proof as to the Eckmann-Schopf proof.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 7 , Issue 3 , September 1964 , pp. 415 - 423
Copyright
Copyright © Canadian Mathematical Society 1964

References

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