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.

irreducible ideal