# Projection on Cartesian Product of Modules

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## Theorem

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

Then for each $j \in \closedint 1 n$, the projection $\pr_j$ 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 $28.7$