A nonzero ring 
whose only (two-sided) ideals are
itself and zero. Every commutative simple
ring is a field. Every simple ring is a prime
ring.
Simple Ring
See also
Field, Ideal, Prime Ring, RingExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Simple Ring." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SimpleRing.html