Short modules and almost noetherian modules - Bilhan, G.; Smith, P. F. (MATHEMATICA SCANDINAVICA, 2006)
It is proved that, for any ring R, a right R-module M has the property that, for every submodule N, either N or M/N is Noetherian if and only if M contains submodules K L such that M/K and L are Noetherian and K/L is almost Noetherian.