Principal ideal

Remarks

The left ideal generated by $a$ is $R a = \{r a : r \in R\}$. If $R$ is commutative, the principal ideal $(a)$ is the set of the multiples of $a$. Every ideal of $\mathbb{Z}$ is principal: each one is $n\mathbb{Z}$ for some integer $n \ge 0$. In $\mathbb{Z}[x]$, the ideal $(2, x)$ is not principal.