Editing Sequence (section)

====Exact sequences====
{{Main|Exact sequence}}
In the context of [[group theory]], a sequence
:<math>G_0 \;\overset{f_1}{\longrightarrow}\; G_1 \;\overset{f_2}{\longrightarrow}\; G_2 \;\overset{f_3}{\longrightarrow}\; \cdots \;\overset{f_n}{\longrightarrow}\; G_n</math>
of [[group (mathematics)|groups]] and [[group homomorphism]]s is called '''exact''', if the [[Image (mathematics)|image]] (or [[Range of a function|range]]) of each homomorphism is equal to the [[Kernel (algebra)|kernel]] of the next:
:<math>\mathrm{im}(f_k) = \mathrm{ker}(f_{k+1})</math>

The sequence of groups and homomorphisms may be either finite or infinite.

A similar definition can be made for certain other [[algebraic structure]]s. For example, one could have an exact sequence of [[vector space]]s and [[linear map]]s, or of [[module (mathematics)|modules]] and [[module homomorphism]]s.