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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

© 1996-9 Eric W. Weisstein