Definition: Let $R$ be a ring, $a\in R$. The principal ideal $M=\langle a \rangle$ consists of all elements of the form $ra+as+na+\sum_{i=1}^{m} r_ias_i$
I know that a left principal ideal $M=Ra=\{ra:r\in R\}$
I know that a right principal ideal $M=aR=\{ar:r\in R\}$
I know that a two-sided principal ideal $M=RaR=\{r_ias_i:r_i,s_i\in R\}$
Intuitively I see why "$ra$" and "$as$" and "$\sum_{i=1}^{m} r_ias_i$" are in the set defined above, but why did Hungerford include "$na$"?
Any help is greatly appreciated!