I suppose that this is a very basic question, but I couldn't find anything precise online. Let $R$ be a ring, and take an $R$-module $M$; assume also that $M$ is finitely generated, by a set of cardinality $n$. How do I prove that, if I take $m$ elements of $M$, with $m>n$, they can't be linearly independent?
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1Does this answer your question? Linearly independent elements are less than generators in a module. – Bonnaduck Nov 01 '21 at 18:37