Definition 6

Let $A$ be a ring and $a$ a two-sided ideal of $A$. The quotient ring of $A$ by $a$, denoted by $A/a$, is the quotient set of $A$ by the equivalence relation $x \equiv y(a)$, with addition and multiplication the quotients of those on $A$.

The ring $A/\{0\}$ is isomorphic to $A$ and $A/A$ is a zero ring.