Noetherian and Artinian Lattices - Derya Keskin Tütüncü; Sultan Eylem Toksoy; Rachid Tribak (International Journal of Mathematics and Mathematical Sciences)
It is proved that if L is a complete modular lattice which is compactly generated, then Rad(L)/0 is Artinian if, and only if for every small element a of L, the sublattice a/0 is Artinian if, and only if L satisfies DCC on small elements.