Given an ideal 
, a semiprime ring is one for which 
implies 
for any positive 
. Every prime ring is semiprime.
Semiprime Ring
See also
Prime Ring, Semiprime IdealExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Semiprime Ring." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SemiprimeRing.html