Let $R$ ba a commutative ring with unity and let $M$ be a $R$-module. For each $m,n\in M$ consider free spaces $\bar{m}$ and $\bar{n}$ generated respectively by $m$ and $n,$ i.e $$\bar{m}=Lin_{R}\{m\}=\{rm:r\in R\}\hspace{5pt}\text{and}\hspace{5pt}\bar{n}=Lin_{R}\{n\}=\{rn:r\in R\}.$$ Additionally let the $\phi_{m,n}:\bar{m}\rightarrow\bar{n}$ be $R$ linear and such that $$\phi_{m,n}(m)=n$$ whenever it can be constructed. Define a following set $$M^!:=\{m\in M:\forall(n\in M)(\phi_{m,n}\text{ can be constructed and is an epimorphism})\}.$$ My question is about a name of this set. More, where can I find some information about it?
EDIT
After the Matt Samuel's comment I feel that saying: "$\phi_{m,n}$ is en epimorphism" is redundant.