universal coefficient theorem


The Universal Coefficient Theorem for homologyMathworldPlanetmathPlanetmath expresses the homology groups with coefficients in an arbitrary abelian groupMathworldPlanetmath G in terms of the homology groups with coefficients in ℤ.

Theorem (UniversalPlanetmathPlanetmathPlanetmath Coefficients for Homology)
Let K be a chain complexMathworldPlanetmath of free abelian groupsMathworldPlanetmath, and let G any abelian group. Then there exists a split short exact sequence

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