prime ring

A ring $R$ is said to be a prime ring if the zero ideal is a prime ideal.

If a prime ring $R$ is commutative, then it is a cancellation ring. If in $R$ has a multiplicative identity $1\ne 0$, then it is an integral domain.

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