The SlugMath Wiki is under heavy development!

Def/Principal ideal

Definition of Principal: Suppose that $R$ is an ideal, and $I$ is an ideal in $R$. Then, $I$ is called a principal ideal if there exists $r \in R$ such that:

• $I = (r)$, where $(r)$ is the set of multiples of $r$ in $R$.

In this case, we say that $I$ is the principal ideal generated by $r$.

Logical Connections

This definition logically relies on the following definitions and statements: Def/Ideal

The following statements and definitions logically rely on the material of this page: Def/PID, and State/Divisibility corresponds to containment of principal ideals

To visualize the logical connections between this definition and other items of mathematical knowledge, you can visit any of the following clusters, and click the "Visualize" tab: Clust/Basic ring theory