Any finite Abelian group is Artinian module over any ring $R$?

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Finite Abelian groups are Artinian as modules over $\mathbb{Z}$

It is known that if a module $M$ has finitely many submodules it has to be Artinian. So above statement can be implied by this right! Can I also replace $\mathbb{Z}$ with any ring $R$ (assuming $M$ is a module over $R$)?