Encyclopedia > Chain complex

Article Content

Chain complex

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...

All Wikipedia text is available under the terms of the GNU Free Documentation License

Search Encyclopedia

Search over one million articles, find something about almost anything!

Featured Article

Thomas a Kempis

... their "exercises." John Wesley and John Newton put it among the works that influenced them at their conversion. General Gordon carried it with him to the battlefield. ...