A ring for which the product of any pair of ideals is zero only if one of the two ideals is zero. All simple rings are prime.
Prime Ring
See also
Ideal, Ring, Semiprime Ring, Simple RingExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Prime Ring." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PrimeRing.html