⊕-Supplemented Lattices

Abstract

In tliis work, ⊕-supplemented and strongly ⊕-supplemented lattices are defined and investigated some properties of these lattices. Let L be a lattice and 1 = a<inf>1</inf> ⊕ a<inf>2</inf> ⊕ ... ⊕ a<inf>n</inf> with a<inf>1</inf>, a<inf>2</inf>,..., a<inf>n</inf> ∉ L. If a<inf>i</inf>/0 is ⊕-supplemented for each i = 1,2,..., n, then L is also ⊕-supplemented. Let L be a distributive lattice and 1 = a<inf>1</inf>⊕a<inf>2</inf> ⊕ ... ⊕ a<inf>n</inf> with a<inf>1</inf>, a<inf>2</inf>,....,a<inf>n</inf> ε L. If a<inf>i</inf>/0 is strongly ⊕-supplemented for each i = 1,2,..., n, then L is also strongly ⊕-supplemented. A lattice L has (D1) property if and only if L is amply supplemented and strongly ⊕-supplemented. © 2019 Miskolc University Press.