Generalized Supplemented Lattices

Abstract

In this work, we define (amply) generalized supplemented lattices and investigate some properties of these lattices. In this paper, all lattices are complete modular lattices with the smallest element 0 and the greatest element 1. Let L be a lattice, 1 = a<inf>1</inf> ∨ a<inf>2</inf> ∨ . . .∨ a<inf>n</inf> and the quotient sublattices a<inf>1</inf>/0, a<inf>2</inf>/0,. . ., a<inf>n</inf>/0 be generalized supplemented, then L is generalized supplemented. If L is an amply generalized supplemented lattice, then for every a ∈ L, the quotient sublattice 1/a is amply generalized supplemented. © 2018 Miskolc University Press.