short exact sequence

Definition

Special properties

Behavior with tensoring in $R$-mod

Let

$$0\to M_1\stackrel{f}{\to }{M}_2\stackrel{g}{\to }{M}_3\to 0$$

be a short exact sequence of R-modules. Then using the tensor product,

$$M{\otimes }_{R}N\stackrel{f\otimes id}{\to }{M}_2{\otimes }_{R}N\stackrel{g\otimes id}{\to }{M}_3{\otimes }_{R}N\to 0$$

is exact.

Proof

todo