There was a prior question regarding intuiting Nakayama's Lemma:
I am currently studying Reid's "Undergrad. Commutative Algebra." His statement of the lemma is specifically in the context of a local ring $(A,m)$ where in his notation, $m$ is the maximal ideal, M is a finite $A$-module; then $M = mM$ implies that $M = 0$.
I feel this question is probably quite naive, so forgive a self-studier:
Can you not simply say that in this case, $m$ has no units, so the only way for
$M = mM$ is for $M$ to be $0$? Thanks.