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Irreducible Ring


A ring in which the zero ideal is an irreducible ideal. Every integral domain R is irreducible since if I and J are two nonzero ideals of R, and a in I, b in J are nonzero elements, then ab is a nonzero element of I intersection J, which therefore cannot be the zero ideal.


See also

Irreducible Ideal, Irreducible Module, Ring

This entry contributed by Margherita Barile

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Cite this as:

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

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