Let $X$ be a chain complex of free R modules. Let $Z_n=\ker(d_n)$ and $B_n=\operatorname{Im}(d_{n+1})$ where $d_n :\to X_n \to X_{n-1}$. Then how can I conclude that the short exact sequence $0 \to Z_n \to X_n \to B_{n-1} \to 0$ is split? How can we write $X_n=Z_n \oplus B_{n-1}$?
Please help me