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Irreducible ideal

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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
How to Cite This Entry:
Irreducible ideal. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Irreducible_ideal&oldid=42014