Definition 6.3.1 (Regular Ideals).label Let $\frak{m}$ be an ideal of $A$ then $\frak{m}$ is regular if $\exists e\in A$ such that $\fall x\in A$ $ex-x\in\in\frak{m}$. Equivalently the quotient algebra $A/\frak{m}$ admits an identity. The element $e\in A$ is called an identity modulo $\frak{m}$.