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A Module is Flat if and Only if its Character Module is Injective

Published online by Cambridge University Press:  20 November 2018

J. Lambek
J. Lambek*
Affiliation:
McGill University and Canadian Mathematical Congress Summer Institute
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The purpose of this expository note is to establish the fact mentioned in the title. While this is not difficult and requires no new ideas, it seems worth doing, as such a simple characterization does not appear explicitly in a recent treatise on the subject of flat modules [Bourbaki XXVII, Chapter 1].

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 7 , Issue 2 , June 1964 , pp. 237 - 243
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Bourbaki, N.,XXVII,Algébre Commutative, Paris 1961.Google Scholar
2. Cartan, H. and Eilenberg, S., Homological Algebra, Princeton 1956.Google Scholar
3. Northcott, D.G., An Introduction to Homological Algebra, Cambridge 1960.Google Scholar