Homology with Arbitrary Coefficient Groups

  • William S. Massey
Part of the Graduate Texts in Mathematics book series (GTM, volume 70)


This chapter is more algebraic in nature than the preceding chapters. In §2 we discuss chain complexes. This discussion mainly puts on a formal basis many facts that the reader must know by now. Nevertheless, there is some point to a systematic organization of the ideas involved, and certain new ideas and techniques are introduced. The remainder of the chapter is concerned with homology groups with arbitrary coefficients. These new homology groups are a generalization of those we have considered up to now. In the application of homology theory to certain problems they are often convenient and sometimes necessary.


Abelian Group Direct Summand Chain Complex Homology Group Short Exact Sequence 
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Bibliography for Chapter V

  1. [1]
    H. Cartan and S. Eilenberg, Homological Algebra, Princeton University Press, Princeton, 1956, Chapter VI, §1.MATHGoogle Scholar
  2. [2]
    P. Hilton and U. Stammbach, A Course in Homological Algebra Springer-Verlag New York, 1971, pp. 112–115.MATHGoogle Scholar
  3. [3]
    S. Mac Lane, Homology, Springer-Verlag, New York, 1963, Chapter V, §6.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1980

Authors and Affiliations

  • William S. Massey
    • 1
  1. 1.Department of MathematicsYale UniversityNew HavenUSA

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