author={Samuel Eilenberg and Saunders Maclane},
  journal={Transactions of the American Mathematical Society},
with d[x]=0. It is convenient to augment ^4°(II) by regarding the commutator quotient group 11/ [II, II] as the group of O-dimensional chains, with d[x]=x[n, TI]. The complex ^4°(I1) occurs in a topological problem in which IT plays the role of the fundamental group of a space. An analogous problem in which the fundamental group is replaced by a higher homotopy group has led us to believe that there exists for abelian groups a specific homology theory distinct from the one described above for… 
Chapter 13. Mac Lane (co)homology
The second Hochschild cohomology group of rings (that is algebras over k = Z) classifies the extensions of a ring by a bimodule provided that the ex­ tensions are split as abelian groups. In order to
On The Homology Theory Of Abelian Groups
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Cohomology theory of abelian groups and homotopy theory I.
  • S. Eilenberg, S. Maclane
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1950