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On the chain equivalence of projective chain complexes

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We obtain a necessary and sufficient condition for n-dimensional chain complexes composed of finitely generated projective modules to be stabilized by free modules to chain equivalence.

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References

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    W. Cockcroft and R. Swan, “On the homotopy type of certain two-dimensional complexes,” Proc. London Math. Soc., 11, 193–202 (1961).

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    C. Faith, Algebra: Rings Modules and Categories. I [Russian translation], Mir, Moscow (1977).

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    K. S. Brown, Cohomology of Groups [Russian translation], Nauka, Moscow (1987).

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    V. V. Sharko, Functions on Manifolds (Algebraic and Topological Aspects) [in Russian], Naukova Dumka, Kiev (1990).

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Author information

Correspondence to N. A. Khmel’nitskii.

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 6, pp. 826–835, June, 2012.

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Khmel’nitskii, N.A. On the chain equivalence of projective chain complexes. Ukr Math J 64, 948–957 (2012). https://doi.org/10.1007/s11253-012-0690-5

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Keywords

  • Exact Sequence
  • Commutative Diagram
  • Chain Complex
  • Projective Module
  • Free Module