g-Supplemented lattices

In this work, g-supplemented lattices are defined and some properties of these lattices are investigated.g-small submodules and g-supplemented modules are generalized to lattices.Let L be a lattice and 1 = a 1 ∨ a 2 ∨ ... ∨ a n with a i ∈ L (1 ≤ i ≤ n).If a i /0 is g-supplemented for every i = 1, 2, ..., n, then L is also g-supplemented.If L is g-supplemented, then 1/a is also g-supplemented for every a ∈ L. It is also defined the g-radical of a lattice L and it is shown that if L is g-supplemented, then 1/r g (L) is complemented.