prime ring

A ring R is said to be a prime ringMathworldPlanetmath if the zero idealMathworldPlanetmathPlanetmath is a prime idealMathworldPlanetmathPlanetmathPlanetmath.

If a prime ring R is commutativePlanetmathPlanetmathPlanetmath, then it is a cancellation ring. If in R has a multiplicative identityPlanetmathPlanetmath 10, then it is an integral domainMathworldPlanetmath.

Title prime ring
Canonical name PrimeRing
Date of creation 2013-03-22 11:51:05
Last modified on 2013-03-22 11:51:05
Owner Wkbj79 (1863)
Last modified by Wkbj79 (1863)
Numerical id 10
Author Wkbj79 (1863)
Entry type Definition
Classification msc 16U99
Classification msc 16N60
Related topic ZeroIdeal