Irreducible ideal

An ideal $I$ in a ring which cannot be expressed as the intersection of two strictly larger ideals: that is, $I = J \cap K \Rightarrow I=J \ \text{or}\ I=K$.

References

[1]	D.G. Northcott, "Ideal Theory", Cambridge Tracts in Mathematics 42 Cambridge University Press ISBN 0-521-60483-4 p.21