Principal Ideal

An Ideal $I$ of a Ring $R$ is called principal if there is an element $a$ of $R$ such that

$$I = aR = \{ ar: r \in R \}.$$

In other words, the Ideal is generated by the element $a$. For example, the Ideals $n\Bbb{Z}$ of the Ring of Integers $\Bbb{Z}$ are all principal, and in fact all Ideals of $\Bbb{Z}$ are principal.

See also Ideal, Ring