Let $R$ be a 'nice' ring (whatever that means, I guess commutative with unity $1_R$) and let $M$ be an $R$--module. Is there a name for the following property?
An element $m \in M$ is called ... iff. whenever we have $m = rm'$ for some $r \in R, m' \in M$ (i.e. if it is a multiple of some other element) then $r$ is a unit.
This seems to correspond to the concept of irreducibility when $M=R$.
Thanks,
FW