I am trying to find out what is meant by $\ker (M)$ where $M$ is a left module of a ring $R$. Apparently it is the subgroup of (?) that acts trivially on $M$ so this to me means the subset of $R$ such that $rm=m $ for all $m$ in $M$.
If this is the case, a couple questions arise. Firstly when it says subgroup, wouldn’t that mean it has to be a subgroup of $R^*$. Secondly if $r \in R$ such that $rm=m $ for all $m \in M$ then does this mean that $r$ is a unit in $R$?