G-SUPPLEMENTED LATTICES

Abstract

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) boolean OR a(2) boolean OR ... boolean OR a(n) with a(i) is an element of 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 is an element of 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.