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 annihilatorPlanetmathPlanetmathPlanetmathPlanetmath of X in R.

We say that R is a left (right) primitive ring if the zero idealMathworldPlanetmathPlanetmath 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