The subset $\{0\}$ of a ring $R$ is the least two-sided ideal of $R$ . As a principal ideal, it is often denoted by $$(0)$$ and called the zero ideal.

The zero ideal is the identity element in the addition of ideals and the absorbing element in the multiplication of ideals. The quotient ring $R/(0)$ is trivially isomorphic to $R$ .

By the entry quotient ring modulo prime ideal, (0) is a prime ideal if and only if $R$ in an integral domain.