prime radical

The prime radical or lower nilradical of a ring R is the intersection of all the prime idealsMathworldPlanetmathPlanetmathPlanetmath of R.

Note that the prime radical is the smallest semiprime idealMathworldPlanetmath of R, and that R is a semiprime ring if and only if its prime radical is the zero idealMathworldPlanetmathPlanetmath.

Title prime radical
Canonical name PrimeRadical
Date of creation 2013-03-22 12:01:29
Last modified on 2013-03-22 12:01:29
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 7
Author CWoo (3771)
Entry type Definition
Classification msc 16N80
Synonym lower nilradical
Related topic RadicalOfAnIdeal
Related topic Nilradical