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
Canonical name	PrimitiveIdeal
Date of creation	2013-03-22 12:01:45
Last modified on	2013-03-22 12:01:45
Owner	antizeus (11)
Last modified by	antizeus (11)
Numerical id	6
Author	antizeus (11)
Entry type	Definition
Classification	msc 16D25
Synonym	primitive ring