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 is irreducible iff or is an irreducible element.

See also

Irreducible Submodule

This entry contributed by Margherita Barile

Explore with Wolfram|Alpha

More things to try:

Cite this as:

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

Subject classifications