primitive ideal

Let $R$ be a ring, and let $I$ be an ideal of $R$.We say that $I$ is a left (right) primitive idealif there exists a simple left (right) $R$-module $X$such that $I$ is the annihilator of $X$ in $R$.

We say that $R$ is a left (right) primitive ringif the zero ideal is a left (right) primitive ideal of $R$.

Note that $I$ is a left (right) primitive idealif and only if $R/I$ is a left (right) primitive ring.