# Projection on Cartesian Product of Modules

## Theorem

Let $G$ be the cartesian product of a sequence $\left \langle {G_n} \right \rangle$ of $R$-modules.

Then for each $j \in \left[{1 \,.\,.\, n}\right]$, the projection $\operatorname{pr}_j$ on the $j$th co-ordinate is an epimorphism from $G$ onto $G_j$.

## Proof

## Sources

- 1965: Seth Warner:
*Modern Algebra*... (previous) ... (next): $\S 28$: Example $28.7$