I'm reading up on the classification of finitely generated modules over principal ideal domains. In doing so, I continuously come up on the statement "Let M be a finitely generated, free R-module."(adsbygoogle = window.adsbygoogle || []).push({});

My question is, is this statement redundant? It seems to me that all finitely generated R-modules are necessarily free as R-modules. In particular, if M is an finitely generated R-module with minimal generating set [itex] A \subseteq M [/itex], then isn't the free R-module on A also M? Or am I missing a technical point?

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# Finitely generated modules as free modules

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