# primitive ideal

Let $R$ be a ring, and let $I$ be an ideal of $R$. We say that $I$ is a left (right) primitive ideal if 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 ring if the zero ideal is a left (right) primitive ideal of $R$.

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

Title primitive ideal PrimitiveIdeal 2013-03-22 12:01:45 2013-03-22 12:01:45 antizeus (11) antizeus (11) 6 antizeus (11) Definition msc 16D25 primitive ring