Why the formula given to a cyclic R-module C changes to Ra, when R has identity and C is unitary. How can I prove that  the formula given to a cyclic R-module C changes to Ra, when R has identity and C is unitary, could anyone help me please?


By definition, $Ra$ is contained in $C$, so it suffices to show $C\subset R$ if $R$ has unity and if $C$ is unitary. But now 
$$
ra+na=ra+(a+a+\dots+a);
$$
can you go from here? By definition of $Ra$, you only need to show that the above element is of the form $sa$, for some $s\in R$. 
