Let $R$ a ring and $M$ a $R-$module. Is $M$ an ideal of $R$ ? And conversely, if $I$ is an ideal of $R$ is it a $R-$module ? To me, I'd say yes (obviously), but a friend of mine told me that it's wrong... So I just want your opinion.
2026-04-21 16:44:05.1776789845
If $M$ a $R-$module, is it an ideal of $R$?
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Certainly not, as $M$ might not even be a subset of $R$. For example, $\mathbb Z^2$ is a $\mathbb Z$-module.