On Amply G-Supplemented Lattices

Abstract

In this work, all lattices are complete modular lattices with the greatest element 1 and the smallest element 0. Let L be a lattice and a ∈ L. If for every b ∈ L such that a ∨ b = 1, a has a g-supplement x in L such that x ≤ b, then we say a has ample g-supplements in L. If every element of L has ample g-supplements in L, then L is called an amply g-supplemented lattice (See [7]). In this work, some properties of these lattices are investigated. © Palestine Polytechnic University-PPU 2022.