Unitary R-Modules with n-Element Bases are Isomorphic

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Theorem

Let $G$ and $H$ be unitary $R$-modules for some ring with unity $R$.

Let $G$ and $G$ both have bases with $n$ elements.

Then $G$ and $H$ are isomorphic.


Proof

From Isomorphism from $R^n$ via $n$-Term Sequence, both $G$ and $H$ are isomorphic to the $R$-module $R^n$.

$\blacksquare$


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