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Extensions of Modules

  • F. E. A. JohnsonEmail author
Chapter
  • 941 Downloads
Part of the Algebra and Applications book series (AA, volume 17)

Abstract

In this chapter we develop the classical theory of module extensions and, in particular, its interpretation in terms of cohomology. As explained in the Introduction, to achieve our intended application it is necessary to avoid injective modules. In consequence a feature of our treatment is the development of the exact sequences of Ext using only projective modules.

Keywords

Exact Sequence Commutative Diagram Short Exact Sequence Projective Module Projective Resolution 
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References

  1. 5.
    Baer, R.: Erweiterung von Gruppen und ihren Isomorphismen. Math. Z. 38, 375–416 (1934) MathSciNetCrossRefGoogle Scholar
  2. 13.
    Cartan, H., Eilenberg, S.: Homological Algebra. Princeton University Press, Princeton (1956) zbMATHGoogle Scholar
  3. 68.
    MacLane, S.: Homology. Springer, Berlin (1963) zbMATHGoogle Scholar
  4. 101.
    Yoneda, N.: On the homology theory of modules. J. Fac. Sci. Tokyo, Sect. I 7, 193–227 (1954) MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity College LondonLondonUK

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