A ring in which the zero ideal is an irreducible ideal. Every integral
domain 
is irreducible since if 
and 
are two nonzero ideals of 
, and 
, 
are nonzero elements, then 
is a nonzero element of 
, which therefore cannot be the zero
ideal.
Irreducible Ring
See also
Irreducible Ideal, Irreducible Module, RingThis entry contributed by Margherita Barile
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Cite this as:
Weisstein, Eric W., with contributions by Margherita Barile. "Irreducible Ring." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/IrreducibleRing.html