Rad-®-Supplemented Lattices

Abstract

In this work, we define Rad- & REG; -supplemented and strongly Rad- & REG; -supplemented lattices and give some properties of these lattices. We generalize some properties of Rad- & REG; -supplemented modules to lattices. Let L be a lattice and 1= a1 & REG;a2 & REG; ... & REG;an with a1, a2, ... , an E L. If ai/0 is Rad- & REG; - supplemented for every i = 1, 2, ... , n, then L is also Rad- & REG; - supple-mented. Let L be a distributive Rad-& REG;-supplemented lattice. Then 1/u is Rad-& REG;-supplemented for every u E L. We also define completely Rad- & REG; -supplemented lattices and prove that every Rad- & REG; -supplemented lattice with SSP property is completely Rad- & REG; - supplemented.