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:
Barile, Margherita. "Irreducible Ring." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/IrreducibleRing.html