Projection on Cartesian Product of Modules

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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