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 December 8th, 2008, 07:44 PM #1 Newbie   Joined: Nov 2008 Posts: 6 Thanks: 0 commutative diagram, module homomorphisms Suppose is a commutative diagram of $R$-modules and $R$-module homomorphisms. (a) Suppose that $\phi$ is injective. Prove that the map $\phi_0 : \text{Ker } f \rightarrow \text{Ker } g$ is injective. (b) Suppose that $\psi$ is surjective. Prove that the map $\bar{\psi} : \text{Coker } f \rightarrow \text{Coker } g$ is surjective.

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