Chain complex
From Wikipedia, the free encyclopedia.

In homological algebra, a chain complex is a sequence of abelian groups or modules A₀, A₁, A₂... connected by homomorphisms d_n : A_n -> A_n-1, such that the composition of any two consecutive maps is zero: d_n o d_n+1 = 0 for all n. Chain complexes are mainly used to define homology and cohomology.

Examples from topology, group theory...

The original article can be found at: http://en.wikipedia.org/wiki/Chain_complex.
All text is available under the terms of the GNU Free Documentation License.