simple ring

A nonzero ring R is said to be a simple ringMathworldPlanetmath if it has no (two-sided) ideal other then the zero idealMathworldPlanetmathPlanetmath and R itself.

This is equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmath to saying that the zero ideal is a maximal idealMathworldPlanetmathPlanetmath.

If R is a commutative ring with unit, then this is equivalent to being a field.

Title simple ring
Canonical name SimpleRing
Date of creation 2013-03-22 11:51:07
Last modified on 2013-03-22 11:51:07
Owner antizeus (11)
Last modified by antizeus (11)
Numerical id 9
Author antizeus (11)
Entry type Definition
Classification msc 16D60