On Supplement Elements in Lattices

Abstract

In this work, some properties of supplement elements in lattices are investigated. Some relation between lying above and (weak) supplement elements also studied. Some properties of supplement submodules in modules which given in [8] are generalized to lattices. Let a be a supplement of b in a lattice L. If a=0 has at least one maximal .(≠a) element, then it is possible to define a bijective map between the maximal elements .(≠a) of a=0 and the maximal elements .(≠a) of 1=b. Let a be a supplement element in a lattice L. If L is amply supplemented, then a=0 is also amply supplemented. If L is weakly supplemented, then a=0 is also weakly supplemented. © 2019 Miskolc University Press.