Editing Split exact sequence (section)

==Examples==
A trivial example of a split short exact sequence is 
:<math>0 \to M_1 \mathrel{\stackrel{q}{\to}} M_1\oplus M_2 \mathrel{\stackrel{p}{\to}} M_2 \to 0</math>
where <math>M_1, M_2</math> are ''R''-modules, <math>q</math> is the canonical injection and <math>p</math> is the canonical projection.
 
Any short exact sequence of [[vector space]]s is split exact. This is a rephrasing of the fact that any [[Set (mathematics)|set]] of [[linearly independent]] vectors in a vector space can be extended to a [[Basis (linear algebra)|basis]].

The exact sequence <math>0 \to \mathbf{Z}\mathrel{\stackrel{2}{\to}} \mathbf{Z}\to \mathbf{Z}/ 2\mathbf{Z} \to 0</math> (where the first map is multiplication by 2) is not split exact.