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Irreducible Ideal


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 I=<a> is irreducible iff a=0 or a is an irreducible element.


See also

Irreducible Submodule

This entry contributed by Margherita Barile

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Cite this as:

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

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