A proper ideal of a ring that is not the intersection of two ideals which properly contain it. In a principal
ideal domain, the ideal 
is irreducible iff 
or 
is an irreducible element.
Irreducible Ideal
See also
Irreducible SubmoduleThis entry contributed by Margherita Barile
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Barile, Margherita. "Irreducible Ideal." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/IrreducibleIdeal.html