Linear Transformation of Generated Module

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Theorem

Let $G$ and $H$ be $R$-modules.

Let $\phi$ and $\psi$ be linear transformations $G$ into $H$.

Let $S$ be a generator for $G$.

Suppose that $\forall x \in S: \phi \left({x}\right) = \psi \left({x}\right)$.


Then $\phi = \psi$.


Proof


Also see


Sources