N is a module and M & L are submodules of N
I want to show that $\beta$ is injective but am having trouble understanding why the exact sequence above implies injectivity.
Asked
Active
Viewed 18 times
0
-
What is the kernel of the map $L \to \operatorname{Ker}(\beta)$? – Michael Albanese Mar 14 '22 at 07:58
-
@MichaelAlbanese since the image of previous morphism is identity then kernel of $L \to \operatorname{Ker}(\beta)$ is L ? – TI99 Mar 14 '22 at 08:08
-
1Ok I got it , thanks ,using factorisation theorem $0 \cong \operatorname{Ker}(\beta) $ – TI99 Mar 14 '22 at 08:21