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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


$ K\sb{3}$ of a ring is $ H\sb{3}$ of the Steinberg group

Author: S. M. Gersten
Journal: Proc. Amer. Math. Soc. 37 (1973), 366-368
MSC: Primary 18F25
MathSciNet review: 0320114
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Abstract | References | Similar Articles | Additional Information

Abstract: A proof of the result of the title is given using standard results of algebraic topology.

References [Enhancements On Off] (What's this?)

  • [1] Emmanuel Dror, A generalization of the Whitehead theorem, Symposium on Algebraic Topology (Battelle Seattle Res. Center, Seattle, Wash., 1971) Springer, Berlin, 1971, pp. 13–22. Lecture Notes in Math., Vol. 249. MR 0350725 (50 #3217)
  • [2] Michel A. Kervaire, Multiplicateurs de Schur et 𝐾-théorie, Essays on Topology and Related Topics (Mémoires dédiés à Georges de Rham), Springer, New York, 1970, pp. pp 212–225 (French). MR 0274558 (43 #321)
  • [3] S. Mac Lane, Homology, Die Grundlehren der math. Wissenschaften, Band 114, Academic Press, New York; Springer-Verlag, Berlin, 1963. MR 28 #122.
  • [4] Daniel Quillen, Cohomology of groups, Actes du Congrès International des Mathématiciens (Nice, 1970) Gauthier-Villars, Paris, 1971, pp. 47–51. MR 0488054 (58 #7627a)
  • [5] -, Cohomology of groups and algebraic K-theory, Amer. Math. Soc. Winter Meeting, Atlantic City, N.J., 1971.
  • [6] R. G. Swan, Algebraic 𝐾-theory, Lecture Notes in Mathematics, No. 76, Springer-Verlag, Berlin-New York, 1968. MR 0245634 (39 #6940)

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Additional Information

PII: S 0002-9939(1973)0320114-8
Keywords: $ {K_3}$ of a ring, Steinberg group, third homology group of a group, central extension
Article copyright: © Copyright 1973 American Mathematical Society

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