Canonical Injection into 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 canonical injection $\operatorname{in}_j$ from $G_j$ into $G$ is a monomorphism.
Proof
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Sources
- Seth Warner: Modern Algebra (1965): $\S 28$: Example $28.7$
