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Irreducible Submodule


A submodule N of a module M that is not the intersection of two submodules of M in which it is properly contained. In other words, for all submodules N_1 and N_2 of M,

 N=N_1 intersection N_2==>N_1=N or N_2=N.

Using a less common terminology, this is equivalent to requiring that the quotient module M/N be meet-irreducible.


See also

Irreducible Ideal

This entry contributed by Margherita Barile

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References

Matsumura, H. Commutative Ring Theory. Cambridge, England: Cambridge University Press, p. 40, 1989.

Referenced on Wolfram|Alpha

Irreducible Submodule

Cite this as:

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

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